Diego Pescarini

Michele Loporcaro

Giampaolo Salvi

Roberta D ' Alessandro

Adam Ledgeway

Luigi Rizzi

Diana Passino

Cecilia Poletto

Andrea Scala

Rita Manzini

Leonardo Savoia

Microvariation in verbal and nominal agreement: An analysis of two Lombard Alpine dialects

Keywords: agreement, concord, microvariation, mesoclisis, metathesis, adjunction, labeling, Italo-Romance

In Bregagliotto and Mesolcinese, two Lombard Alpine dialects, feminine plural agreement/concord is marked by the formative -n, a reflex of the 3rd person plural verbal ending. In Bregagliotto, plural -n triggers mesoclisis of the feminine subject clitic in contexts of inversion, whereas in the noun phrase -n behaves as a second-position element marking plural feminine concord. Mesolcinese exhibits verbal gender agreement as the formative -n occurs on the inflected verb whenever a feminine plural subject or the feminine plural object clitic occurs; in feminine plural DPs, -n is attached to any element except the definite article. I argue that the Bregagliotto system emerged when -n was reanalysed as an adjunct pluraliser, whereas in Mesolcinese -n has been turned into a marker of morphophonological concord/agreement.

Introduction

This article deals with agreement in two Italo-Romance (groups of) dialects that are spoken in two valleys of southern Switzerland: the Mesolcina and the Bregaglia valley. Although both 3 -N marking is asymmetric and, at first sight, the asymmetry in one variety seems the mirror image of the asymmetry in the other: in Mesolcinese the suffix -n tends to occur on the rightmost elements in the DP, whereas in Bregagliotto -n usually occurs on determiners, see (1)a.

-In both varieties, -n (which is a reflex of the 3rd person plural verbal ending) occurs on finite verbs. In Mesolcinese -n occurs if and only if either the subject, see (1)b, or the object, see (1)c, are feminine plural. In Bregagliotto, conversely, -n occurs with all 3 rd person plural subjects regardless of their gender, see (1)b, and it never marks object agreement.

(1) a. nominal agreement: 1991[START_REF] Ritter | Cross-linguistic evidence for number phrase[END_REF][START_REF] Bernstein | DP's in French and Walloon: evidence for parametric variation in nominal head movement[END_REF][START_REF] Picallo | Nominals and nominalizations in Catalan[END_REF] ii) How to account for asymmetric agreement/concord? Various explanations have been discussed in the recent literature to account for variation in asymmetric/partial/"lazy" agreement systems (for an overview, see [START_REF] Stark | Adnominal adjectives in romance. Where morphology seemingly meets semantics[END_REF]. Variation in nominal agreement may depend on where Number is probed/merged/interpreted: D (Delfitto & Schrotten 1991[START_REF] Bouchard | Adjectives, number and interfaces[END_REF], Num [START_REF] Rasom | Lazy concord in the Central Ladin feminine plural DP: A case study on the interaction between morpho-syntax and semantics[END_REF], D or n (Dobrovie-Sorin 2012), D, n orto a lesser extent -A [START_REF] Cyrino | On the Syntax of Number in Romance[END_REF]. Additionally, scholars such as Bonet, Lloret & Mascarò 2015[START_REF] Cyrino | On the Syntax of Number in Romance[END_REF] entertain the hypothesis that asymmetric agree may results from postsyntactic concord, which triggers the externalisation of Number/Gender features within a given Spell-Out domain [START_REF] Cyrino | On the Syntax of Number in Romance[END_REF]: 187; see also [START_REF] Manzini | N morphology and its interpretation: Romance feminine/plural -a[END_REF], Manzini et al. 2021).

iii) How to account for the similarities between clausal agreement and nominal concord?

The idea that the DP and the clause have isomorphic structures has been proposed in [START_REF] Abney | The English Noun-Phrase in its Sentential Aspect[END_REF][START_REF] Ritter | Two functional categories in noun phrases[END_REF][START_REF] Ritter | Cross-linguistic evidence for number phrase[END_REF][START_REF] Bernstein | DP's in French and Walloon: evidence for parametric variation in nominal head movement[END_REF] Salvioni 1902: 139;[START_REF] Keller | Di alcune forme verbali nella parlata di Mesocco[END_REF][START_REF] Sganzini | Di alcune forme verbali nella parlata di Mesocco[END_REF]Jaberg 1951;[START_REF] Tuttle | Per l'origine dei plurali in -n nel Grigioni italiano: poligenesi e parallelismi strutturali[END_REF][START_REF] Loporcaro | Crossing form and function: first and second person plural imperatives in the dialect of Mesocco[END_REF][START_REF] Pescarini | L'accordo asimmetrico nel Grigioni italiano. Convergenze morfologiche e divergenze sintattiche[END_REF]. This article aims to provide a closer comparison between Mesolcinese and Bregagliotto in the light of data from the aforementioned literature, from syntactic atlases (in particular the AIS), and from my own fieldwork notes. I intend to show that Bregagliotto provides crucial evidence to reach a better understanding of Mesolcinese, which exhibits a more innovative and peculiar system.

From a theoretical standpoint, I argue that the agreement phenomena we find in present-day Mesolcinese and Bregagliotto originated from the syntactic reanalysis of a morphophonological irregularity that is still visible in Bregagliotto. In Bregagliotto the plural verbal ending -n undergoes metathesis when it is followed by the feminine plural enclitic la, yielding the order Root > la > -n that is unparalleled in the other Italo-, Gallo-, and Rhaeto-Romance dialects. I argue that this morpho-phonological irregularity triggered a sequence of three cascading changes:

i)
First, -n was reanalysed as an adjunct PLURALISER [START_REF] Wiltschko | The syntax of non-inflectional plural marking[END_REF][START_REF] Dobrovie-Sorin | Number as a feature[END_REF][START_REF] Cyrino | On the Syntax of Number in Romance[END_REF], which is not incorporated by the verb.

ii)

The PLURALISER is merged with Person probes such as T and D [START_REF] Longobardi | Reference to individuals, person, and the variety of mapping parameters[END_REF].

Person probes were thus the pivots triggering the emergence of N-marking in the DP.

iii) Differences between the two varieties result from the status of n: in Bregagliotto n still lexicalises the adjunct PLURALISER, whereas in Mesolcinese it externalises number agreement via morphophonological concord [START_REF] Cyrino | On the Syntax of Number in Romance[END_REF].

The structure of the article is as follows: §2 focuses on metathesis and mesoclisis; §3 and §4 explore a syntactic analysis of the Bregagliotto T and D systems, respectively; §5 argues that in Mesolcinese the formative n is a marker of morphophonological agreement/concord; §6 elaborates on the other properties that distinguish Mesolcinese from Bregagliotto: gender and object agreement on finite verbs; §7 concludes.

The genesis of N marking

The table in (2) compares the distribution of -n in the clause (DPs will be examined in §5): in Mesolcinese, -n is suffixed to the verb whenever a feminine plural subject or object clitic occurs.

Conversely, in Bregagliotto -n is the regular ending of all 3 rd person plural verbs, regardless of the gender of subjects and objects.

( Since mesoclisis is the only anomaly in the distribution of -n and it correlates with the presence of feminine plural subjects, it seems plausible that the pattern in (3)b, (4)b, (5)b played a role in the emergence of N marking. Before exploring this possibility in greater detail (in §3), some remarks on the nature and origin of mesoclisis are in order.

First of all, mesoclisis of subject clitics is unparalleled and, from a syntactic standpoint, it is completely unexpected: it is a widely held view that enclisis results from movement of the inflected verb to the left periphery (say, to Rizzi's 1997 Fin), crossing the position harbouring the subject clitic:

(6) [Fin V+T [SCl [T (V+T)
Since mesoclisis should be impossible under ( 6), to account for Bregagliotto we must invoke a mechanism that "overrides" (6) when the subject is feminine. The most probable explanation is that mesoclisis was initially triggered at PF by metathesis, a phonological change preventing sequences of sonorants. As shown by numerous examples (e.g. dormir > dromir 'to sleep' in (3)), Lombard (Alpine) dialects tend to avoid clusters of sonorants by reversing the order of segments or syllables. Since the feminine plural enclitic la begins with a sonorant, enclisis yielded a marked cluster of consonants (*nl) that was avoided by means of metathesis, see (7)a.

In the masculine, conversely, metathesis did not take place as the sequence formed by the plural ending -n and the masculine plural clitic i is phonologically licit. Consequently, the masculine clitic of Bregagliotto has kept occurring after the agreement ending, see (7)b, as subject enclitics normally do. "syntactic change should not arise, unless it can be shown to be caused-that is, to be a well-motivated consequence of other types of change (phonological changes and semantic changes, including the appearance/disappearance of whole lexical items) or, recursively, of other syntactic changes." (Longobardi 2001: 278) According to this view, which is endorsed by the present work, syntactic change cannot result from the invariable principles of Narrow Syntax, which are by definition inert to change. Innovationsand, consequently, variationis first triggered by reanalysis of interface effects, such as metathesis, which end up modifying the featural endowment of functional elements (where syntactic variation is encoded, according to the so-called Borer-Chomsky Conjecture).

(7) Syntax PF a. [V-n [la → */-nla/ > /-lan/ b. [V-n [i → /-
In this respect, it is worth noting that in Lombard Alpine dialects inversion (and, consequently, mesoclisis) was originally much more pervasive than nowadays. In present-day dialects, inversion is found in interrogative clauses, but for centuries northern Italian dialects displayed traces of verb-second syntax of the kind that is still productive in the nearby Rhaeto-Romance varieties spoken in the Grisons (see Fig. 1). This amounts to saying that, in previous diachronic stages, metathesis was more frequent than nowadays and, given its higher incidence, it could have prompted the kind of syntactic reanalysis reconstructed here.

A syntactic analysis of the Bregagliotto T system

In this section, I entertain the hypothesis that Bregagliotto speakers rebracketed sentences including feminine plural clitics in order to accommodate metathesis. As a consequence, the -n co-occurring with the feminine la was reanalysed as an adjunct PLURALISER [START_REF] Wiltschko | The syntax of non-inflectional plural marking[END_REF].

In origin, the ending -n spelled out T's person and number features that are valued via agree(ment) with the subject. As shown in (9)b, -n is merged in T when T probes a plural subjects such as i 'they.M' (let us assume, for the sake of simplicity, that subject clitics are first merged in v). The formative -n forms a complex head with the verb and, when the latter moves to C, as in (9)e, -n moves along with the verbal root above the subject clitic i, as in the other Romance languages and dialects exhibiting inversion.

(9) a.

b.

c.

d.

e.

[v i drom] [T -n [v i drom]] [T droma-n [v i droma]] [T i [T droma-n [v i droma]]] [C droma-n [T i [T droma-n [v i droma]]]] sleep(x) V-to-T Subj. movement T-to-C (inversion)
Sentences featuring feminine plural subjects hadin originthe same syntactic derivation, until metathesis reversed the order of -n and the feminine enclitic la at PF, yielding a misalignment between syntax and morphology, in (10)f:

(10) a.

b. c.

d.

e.

f. f.

[v la drom] [T -n [v la drom]] [T droma-n [v la droma]] [T la [T droma-n [v la droma]]] [C droma-n [T la [T droma-n [v la droma]]]]
[v la drom]

[T T^n [v la drom]]] [T droma^n [v la droma]]] [T la [T droma^n [v la droma]]]] [C droma [T la [T droma^n [v la droma]]]]] | | /droma la n/ sleep(x)
The PLURALISER is merged with T V-to-T

Subj. movement T-to-C (inversion), ^n is stranded

The PLURALISER ^n modifies the vP (along the lines discussed in Bianchi 2008: §3) that in Bregagliotto does not contain Number information as the subject clitic la pronominalizes either singular or plural entities, e.g. la droma 'she/they sleep(s)'. Hence, the PLURALISER n can be merged when the subject is feminine, but it cannot co-occur with the masculine plural i 'they' that carries its own number feature. By the same token, ^n cannot be merged to T if the subject is 1 st /2 nd person since "apparent number on 1 st and 2 nd person does not instantiate the category Number" (Wiltschko 2008: §2.4.3), a widely held view since [START_REF] Benveniste | Problèmes de linguistique générale[END_REF][START_REF] Lyons | Introduction to theoretical linguistics[END_REF]. In case of masculine subjects and 1 st /2 nd person subjects, plural marking is therefore inflectional 3

There are alternative ways to account for the excorporation of -n. Calabrese and Pescarini 2014 explored a Distributed Morphology analysis in which metathesis triggers fission of feature bundles. In a previous version of this work I argued for an alternative analysis based on D'Alessandro's 2016, 2017 analysis of central Italo-Romance dialects that display agreement phenomena analogous to those of Bregagliotto and Mesolcinesei.e. verbal gender agreement and omnivorous agreement [START_REF] Nevins | Multiple agree with clitics: person complementarity vs. omnivorous number[END_REF]. D'Alessandro argues that dialects showing gender and/or omnivorous agreement exhibit a complex probe formed by T and an extra probe π. However, the analysis proposed in the present work, where I assume that -n becomes an adjunct, seems to me more elegant. in nature, i.e. the verbal ending spells out T's agreement features, whereas, with feminine subjects, plural marking is modificational [START_REF] Wiltschko | The syntax of non-inflectional plural marking[END_REF]. Adjectives and nouns that precede ^n in (12)d-f are not real counterexamples to the hypothesis that ^n is merged in D. In fact, head movement to D is a rather common phenomenon in determiner-less DPs [START_REF] Longobardi | Reference and Proper Names: A Theory of N-Movement in Syntax and Logical Form[END_REF]. In this respect, it is worth noting that many instances of Adj^n or N^n sequences, which nowadays are quite marginal, are found in vocatives, which

A syntactic analysis of the Bregagliotto D system

Espinal 2013 argues to be derived by moving Ns or As to a dedicated position (Voc) above D.

Hence, adjectives and nouns precede -n in (12)d-f because they can move to D (or to an even higher position such as Voc) in determiner-less DPs:

Mesolcinese (vs Bregagliotto): on morphophonological agreement

Mesolcinese differs from Bregagliotto in two related respects:

4

The displacement of personal pronouns in D takes place to value D's Person feature in the same way in which subject move to spec T. If X (that is, a pluralized D) c-commands Y (that is, N or A), which in its turn c-commands Z (N or A), plural marking may be overt on X alone, on X-Y, on X-Y-Z, but not on X-Z.

The above constraint, however, accounts neither for Bregagliotto nor for Mesolcinese. In the former, n behaves as a second position element, in the latter n occurs on any inflected element except definite articles.

Alternatively, Manzini & Savoia's 2019; Manzini et al.'s 2020 argue for a more powerful constraint that affects plural marking in the noun phrase and in the clause in parallel fashion.

For instance, in the Friulian dialect in (24), the definite article and the object clitic never exhibit the sigmatic plural marker that regularly occurs with other elements such as adjectives, nouns, past participles.

Mesolcinese: gender and object agreement on T

Verbal gender agreement is very rare in Romance; it is attested in few dialects scattered along the Alps and in central Italy [START_REF] D'alessandro | Floating Features in Syntax: Person, Deixis and Agreement in Italo-Romance[END_REF][START_REF] D'alessandro | When you have too many features: Auxiliaries, agreement and clitics in Italian varieties[END_REF]. In Mesolcinese, verbal gender agreement arguably emerged when the formative -n marking 3 rd person plural agreement was lost, a phenomenon that is widespread in the nearby Lombard varieties spoken in the basin of the river Ticino (to which the Mesolcina valley belongs, see the map in Fig. 1). In the dialects of Ticino, 3 rd person singular and plural verbal forms became syncretic because the ending -n, marking 3 rd person plural agreement, was lost [START_REF] Salvioni | Del plurale femminile di prima declinazione esposto per -a ed -an in qualche varietà alpina di Lombardia[END_REF]), e.g. kanta-n > kanta 'they sing' = 'he/she sings'.

Mesolcinese varieties were subject to the same innovation, which targeted the (masculine) The only element in (32) that is not subject to morphophonological agreement is the inflected verb, which is also the only element that agrees in Person. This complementary distribution between Person (syntactic) agreement and Gender (morphophonological) agreement has been previously noticed in the literature. For instance, Baker 2008: 85-86 points out that morphophonological agreement and person agreement are somehow in complementary distribution. However, the agreement pattern illustrated in (33), in which a 1 st person singular verb agrees with a feminine plural object clitic, does not corroborate Baker's idea that verbs can agree in number and gender if they lose the ability to agree in person.

Conclusions

This article examined the agreement systems of two Lombard Alpine dialects. In both varieties, feminine plural agreement/concord is marked by the formative n, which resulted from the reanalysis of the 3 rd person plural verbal ending.

The verbal morphology of Bregagliotto is quite regular (save for metathesis that occurs when the inverted subject clitic follows the plural formative -n). Concord within the noun phrase is marked by -n, which always occurs after the first element of the phrase.

Mesolcinese is more complicated as it exhibits verbal gender agreement: the formative -n is attached to the inflected verb when either the subject or the object (clitic) is feminine plural. In the noun phrase, n is attached to any element except the definite article.

As for Bregagliotto, I argued that metathesis was eventually reanalysed, yielding an alternation between two homophonous items: the agreement head -n and the adjunct ^n. The latter carries feminine plural features and, unlike -n, it is not incorporated by the inflected verb.

The formative ^n is merged with person probes such as T and D.

In Mesolcinese, conversely, +n does not lexicalise the adjunct pluraliser, but it is a feminine plural marker involved in morpho-phonological agreement/concord. In Mesolcinese +n combines with all inflected categories within a Spell-Out domain, both at the clausal and DP level [START_REF] Manzini | N morphology and its interpretation: Romance feminine/plural -a[END_REF]. The inflected verb, which, like in other Lombard dialects,

shows no distinction between the 3 rd and 6 th person and can no longer undergo inversion, is

  argue that Number is encoded in a dedicated functional head (e.g. NumP), whereas Dobrovie-Sorin 2012, Cyrino & Espinal 2015, 2020 entertain the hypothesis that the Plural obtains when a modifier is adjoined to the functional spine of DPs. Related issues are the position of the element encoding Number, see (ii), and the nature of the agree relationship between D, N, and other nominal modifiers (see Cyrino & Espinal 2015 on Inverse Agree, Mathieu 2009 on Cyclic Agree).

  argued that inflectional positions such as Number Phrase (NumP) are sandwiched between NP and DP, yielding a layered structure (D > Num/Gen > N) analogous to the clausal one (C > Agr/T > V). The parallelism between DP and CP is revived by Manzini & Savoia's 2019 analysis of Mesolcinese, which revolves around the hypothesis that the externalization of agreement features is sensitive to syntactic phases (Chomsky 2001). The above research questions will be addressed in the light of data from Mesolcinese and Bregagliotto. These Lombard Alpine dialects have been extensively debated in the dialectological literature, most of which focused on the synchronic distribution of -n and its possible etymology, see Ascoli 1875: 269-270, 273-274; Schuchardt 1880:153; Meyer-Lübke 1890(II): §32-33;

  ni/ Although mesoclisis of subject clitics is virtually unattested, similar patterns are found with object clitics in Mexican Spanish varieties (Harris & Halle 2005): (8) has been analysed from both morpho-phonological and syntactic standpoints (see Halle & Harris 2005 vs Kayne 2010). Evidence for a morphological analysis of (8) comes from instances of reduplication, e.g. venda-n-lo-n and free alternations between (8)a and (8)b (for extensive discussion, see Arregi & Nevins 2018). However, neither Bregagliotto nor Mesolcinese show instances of reduplication of the Chicano type; moreover, in Bregagliotto mesoclisis is not optional and, most importantly, mesoclisis correlates with extensive patterns of N-marking in the nominal domain and, in Mesolcinese, with verbal gender agreement. These phenomena cannot be accounted for under a morphophonological analysis of the kind proposed by Halle & Harris 2005. Hence, although it is likely that mesoclisis originated from metathesis, a syntactic analysis of the successive chronological stages seems definitely on the right track.In the next section, I will therefore argue that metathesis triggered reanalysis (i.e. syntactic rebracketing) of -n as an adjunct PLURALISER. This in turn triggered a series of further changes that made Bregagliotto and Mesolcinese diverge from the other Lombard dialects and from each other. The hypothesis that a marginal irregularity reverberated throughout the agreement systems of Bregagliotto and Mesolcinese is consistent with the tenets of[START_REF] Longobardi | Formal Syntax, Diachronic Minimalism, and Etymology: The History of French Chez[END_REF] Inertial Theory of syntactic change, the gist of which is summarised in the following quote:

(

  this irregularity triggered rebracketing: as shown in (11)b-c, n does no longer lexicalise T, but it is adjoined to T. From now on I adopt the symbol ^ (taken from[START_REF] Hornstein | Adjunction, Labeling, and Bare Phrase Structure[END_REF] to distinguish the inflectional marker n, lexicalising T, from the freestanding PLURALISER ^n that is adjoined to T. The latter does not belong to the constituent that is subject to movement(Hornstein & Nunes 2008: 68), possibly because adjuncts are merged "on a separate plane"(Chomsky 2004: 118; see also Chomsky 2020: 47), and is not pied-piped/incorporated by V/T.3

Wiltschko 2008 :

 2008 §2 argues that in several languages number marking is not inflectional, but modificational: the plural obtains by adjoining a PLURALISER to the functional spine of the DP. Dobrovie-Sorin 2012 and Cyrino & Espinal 2020 propose a similar analysis for Romance. In particular, Cyrino & Espinal argue that the PLURALISER is a syntactic adjunct to D; witness languages in which plural marking is morphosyntactically encoded on the determiner, e.g. Br.Port. os livros / os livro / *o livros 'the books', In this section, I argue that the hypothesis of an adjoined PLURALISER accounts for the syntax of n in Bregagliotto, which is exemplified in (12the data in (12), two main questions need elaboration: i) why ^n behaves as a second position element in the DP; ii) how ^n became a marker of nominal concord.The hypothesis that number is encoded by a PLURALISER accounts for the second-position syntax of ^n: since the PLURALISER is merged in D, ^n is correctly predicted to follow all kinds of determiners:(13)[D 'kwela^n [du [ga'li:na]]] 'these two hens'The marker ^n never occurs in indefinite DPs that are introduced by numerals because, as Wiltschko 2008 points out, adjunct pluralisers are incompatible with DPs that are

  emergence of N-marking in the DP, my explanation relies on the isomorphism between clausal/T and nominal/D domains, which has been widely debated in the generative literature since Abney 1987. T and D play a similar role in the two domains, by anchoring the clause/phrase to the context via deictic features such as Tense, Definiteness, and Person. In my opinion, Person is the pivotal feature that allowed the transfer of agreement morphology (namely, of ^n) from the verbal to the nominal domain, as shown in (16). Given the constrained distribution of ^n in (12) one can eventually hypothesise that the PLURALISER n is subcategorised for person (I will resume this discussion in § §5-6). (16) a. [T{Person}^n [ … [nP Root]]] b. [D{Person}^n [ … [vP Root]]] The idea that D, like T, probes Person is supported by evidence of N-to-D movement of pronouns: unlike nouns, personal pronouns bearing Person features move above prenominal modifiers such as numerals in (17) and adjectives in (18) (for further evidence, see Longobardi 2008): 4 (17) a. [D noi [due [N noi]]] (It.) b. [D loro [due [N loro]]] c. [D *amici [due [N amici]]] 'the two of us/the two of them/two friends' (18) a. [D noi [ricchi]] (It.) b. [D we [rich]]To conclude, in this section I argued that the person/number ending -n has been reanalysed as a PLURALISER ^n that is adjoined to T (first) and then to both person probes: T and D. The hypothesis accounts for the extension of ^n to the DP, once we assume that i) D probes Person[START_REF] Longobardi | Reference to individuals, person, and the variety of mapping parameters[END_REF] and ii) in many Romance languages, plural DPs are obtained by merging a PLURALISER in D (Dobrovie Sorin 2012; Cyrino & Espinal 2020). Since ^n is merged with D, it always occurs after the leftmost element of the DP; this accounts for the second-position syntax of the Bregagliotto n.

  2020, I contend that the above differences between Mesolcinese and Bregagliotto result from the morphological mapping of number. Cyrino & Espinal 2020 argue for a principled distinction between pluralisation (in Syntax) and plural marking (in Morphology): the former is conceived of as syntactic modification (i.e. merger of a PLURALISER), while the latter consists of "morphophonological agreement (or concord) among the constituents within the same Spell-out domain" (Cyrino & Espinal 2020: 187). Morphophonological agreement/concord results in the insertion at PF of redundant inflectional exponence, as exemplified in the following examples from Italian (from now on, I will use the symbol + to signal morphophonological exponence)our-FPL dear-FPL friend-FPL are been-FPL left-FPL 'Our nice friends have been left.' Unlike Italian, various Romance languages/dialects exhibit patterns of morphophonological agreement that are partial/asymmetric/lazy, see Stark & Pomino 2009 for an overview. Partial marking is usually sensitive to syntactic constituency; Cyrino & Espinal 2020: 189 propose the following constraint: (23) Plural-marking-on-D constraint

5

  -PL I.have called-FPL 'I have called them.F' In Manzini & Savoia's account, the parallelism between DP and participle agreement is captured by a single parameter that is sensitive to the inner articulation of phases (Chomsky 2001): plural marking is either uniform within the phase or within one of the phase components, the head 5 , the edge, or the complement. The parameter is category-neutral and, in principle, the same parametric choice may determine the distribution of agreement markers in phases (DP, CP, and vP), whichin Manzini & Savoia's analysisare headed by determiners, subject clitics, and object clitics, respectively. Mesolcinese provides strong support for Manzini & Savoia's 2019 parametric model as n occurs on all nominal element except the definite article la, which can therefore introduce either singular or plural feminine DPs: To explain why demonstratives exhibit -n morphology, see (i), one may argue that they are merged in SpecDP and/or they are first merged in the complement of the phrase. On these two options, see Guardiano 2010. (i) kelan mat-an (Mes.) FPL 3.NOM.F= is.FPL milked-FPL 'The cows are milked.' Mesolcinese thus supports the hypothesis of a category-neutral theory of agreement marking, in which a single parameter affect both nominal and verbal domains, as shown in the following table/diagram (from Manzini & Savoia 2019): both Bregagliotto and Mesolcinese exhibit systems of partial N-marking that are isomorphic in the clause and in the DP. However, while in Bregagliotto n lexicalises the otherwise abstract PLURALISER (see § §3-4), in Mesolcinese number is externalised via morphophonological concord within a Spell-Out domain. In the latter, n has the same distribution as other inflectional markers such as F.SG -a and is constrained by a parameter along the line of (27). The difference between the two dialects is shown in the following trees (recall that the symbols ^, + signals syntactic adjunction and insertion at PF, respectively): Building on this hypothesis, the next section seeks to account for the participle-like agreement of Mesolcinese finite verbs, which undergo gender and object-clitic agreement. The gist of the next section is that Mesolcinese finite verbs are subject to morpho-phonological agreement whenever they are in the c-command domain of feminine plural object and/or subject clitics.

  window-FSG it-FSG= they.have washed-FSG all-FSG 'The window, they have washed all of it.' When object clitics are merged in T, participles, predicative adjectives, and quantifiers must/can agree with the cliticon a language-specific basisin the same way in which nouns and nominal modifiers agree in number with D (or, more precisely, with the abstract PLURALISER that is merged in D, see Dobrovie Sorin 2012; Cyrino & Espinal 2020).

  How to account for Number agreement in the (Romance) DP? Scholars such as Ritter

	The data introduced in (1) raise three main research questions:
	i)
		M.SG	M.PL	F.SG	F.PL
	Mesolcinese ɛl sɔ ˈdziːu	i sɔ ˈdziː	la sɔ ˈdziːa	la sɔn ˈdziɐn
	Bregagliotto ɐl se ˈdziːo	i se dziː	lɐ se ˈdziːa	lɐn se ˈdziːa
		'his/her uncle'	'his/her uncles'	'his/her aunt'	'his/her aunts'
	b. verb-subject agreement:
		M.SG	M.PL	F.SG	F.PL
	Mesolcinese ɛl dis	i dis	la dis	la ˈdizɛn
	Bregagliotto ɐl diːʃ	i ˈdiʒɐn	la diːʃ	la ˈdiʒɐn
		'he says'	'they.M say'	'she says'	'they.F say'
	c. verb-object agreement in Mesolcinese:
	la	ˈtʃamiəŋ (Mes.)
	her= I.call-FPL
	'I call them.F'

  2) Distribution of n in the clause:

	(3) a. i/la	ˈdromɐŋ	(Bre.; Manzini & Savoia 2005.I:371)
		3NOM.M.PL/F= sleep-PL	Mesolcinese	Bregagliotto
		a. SCl V 'They.M/F sleep.'	(F) la ˈdizɛn	(F) la 'fyman
		b. 'dromɐŋ-i?	/	(M) i dis ˈdrom-la-ŋ?	(M) i 'fyman
		sleep-PL=3NOM.M.PL	'they say' sleep=3NOM.F=PL	'they smoke'
		b. V SCl 'Do they.M/F sleep?'	* 2	(F) ˈdrom-la-ŋ?
					(M) 'dromɐŋ-i?
	(4) a. l'	an (Bre.; Salvioni 1902: 135)	'do they.f sleep?'
		c. OCl V 3NOM.F=have-PL	la ˈtʃami-əŋ	lan portan
		'They.F have.'		'I call them.f'	'They bring them'
		b. à-la-n?
	Bregagliotto is more conservative than Mesolcinese under three main respects: have=3NOM.F=PL
	i)	In Bregagliotto, verb-subject (clitic) inversion is fully productive; 'Do they.M/F have?'
	ii)		in Bregagliotto, finite verbs never agree in gender with object clitics (as in the vast
	(5) a. l'	majority of Italo-Romance dialects); en
	iii)	Bregagliotto exhibits no gender verbal agreement as verbal morphology is regular (-3NOM.F=be-PL
		n is the 3rd person plural ending of the verb, regardless of the gender of the subject). 'They.F are.'
	The only irregularity displayed by Bregagliotto is that the subject clitic la 'her/they.F' b. e-la-n? (Bre.; Salvioni 1902: 135)
	precedes the formative -n when it is enclitic, yielding a pattern of mesoclisis, cf. (2)b. As shown be=3NOM.F=PL
	in (3)b, (4)b, (5)b), the -n ending of 3 rd person plural verbs always follows the feminine subject 'Are they.M/F?'
	clitic la, while it precedes the masculine clitic -i (as is customary in all the Romance languages
	that show subject clitic inversion, which always yields the order Root > Inflection > inverted
	subject clitic):

  Multiple agreement: While in Bregagliotto ^n always follows Person probes (and, consequently, occurs once in the clause and once in the DP), in Mesolcinese the formative n occurs on all inflected elements in the clause and in the DP (demonstratives, nouns, quantifiers, past participles, etc.), except the clitic/article la. . inflected verbs end in n when they co-occur with a 3 rd person feminine plural object clitic, as in (20); in this case, n occurs regardless of the verb's person

		specification.
		b. verbs at the 3 rd person plural exhibit n if the subject is feminine, otherwise they
		The distribution in the DP is shown in table (19), which compares N-marking in have no ending, see (21);
		Bregagliotto and Mesolcinese:
	(20) la	ˈtʃami-əŋ (Mes.)
	(19) N domain them.F= call.1SG-FPL
	'I call them.F'	Mesolcinese		Bregagliotto
	a. Art + N	la gaˈnasan		lɐn gɐˈnaʃɐ
	(21)	M.SG	'the jaws' M.PL	F.SG	'the jaws' F.PL
	b. Dem + N	kelan mat-an		'kwelan du ga'li:na
			'these girls'		'these two hens'
	c. Q + N	Tanten váken		ˈtantɐm ˈvɔːltɐ
			'many cows'		'many times'
	d. Adj + N	-		povran gnocca
					'poor girls'
	e. Art + N + Adj	la ˈʃpalɛn ˈlarɡɛn		lɐn ˈʃpalˑɐ ˈlaˑrɡɐ
			'the big shoulders'		'the big shoulders'
	f. N (+ Adj)	-		Erban verda!
					'green herbs'
	i)	Participial-like agreement of finite verbs: Mesolcinese finite verbs exhibit two

i)

properties that, in other (Italo)Romance varieties, characterise participle agreement, i.e. object-clitic agreement and gender agreement: a

  person ending -n, but spared the homophonous +n marking morphophonological concord/agreement ( §5). Once the full-fledged Person ending -n was lost, 3 rd person plural verbs became syncretic with 3 rd person singular verbs in the masculine, whereas in the feminine the marker +n kept occurring, yielding the present-day pattern of verbal gender agreement:The change in (29) is not documented in the present indicative, but a similar evolution can be observed in the future, where the emergence of verbal gender agreement is more recent than in the present indicative. According to the data contained in the AIS (which were collectedThe data in (30) and (31) support the hypothesis that "proto-Mesolcinese"like Bregagliotto featured two homophonous endings (-n, ^n): the former has been lost (as in other Lombard dialects), while the latter became a morpho-phonological marker (+n).As argued in §5, the hallmark of morphophonological agreement is the multiple occurrence of plural exponence within a Spell-Out domain. In the remainder of the section, I elaborate on the hypothesis that, besides nominal concord, morphophonological agreement targets past participles, predicative adjectives and floating quantifiers that are in the object clitic's ccommand domain, between square brackets in (32). According to this analysis, past participles therefore agree in the same way in which determiners, adjectives, possessives and other nominal modifiers undergo concord in the DP (cf.Manzini & Savoia's 2019 parameter in (27)):

	(29)	proto-Mes./Breg. Mes.
	a. kanta-n	>	kanta(*-n) 'they.M sing'
	b. kanta-n	>	kanta+n 'they.F sing'
	almost a century ago), the future exhibited the inflectional ending -n with feminine and
	masculine subjects, see (30), until the first half of the 20 th century. Nowadays, the formative -n
	can no longer co-occur with masculine subjects, cf. (31)a, while it is restricted to feminine
	subjects in the future as well as in the present, cf. (31)b:
	(30) i	foràn	kel k'	i	voràn (Mes. AIS)
	they.M= do.FUT.3PL that that they.M= want.FUT.3PL
	'They will do what they will want.'
	(31) a. i	faˈra(*n) kεl k	i	voː(*ran) (Mes. 2017)
		they.M= do.FUT.3PL that that they.M= want.FUT.3PL
	b. la	faˈra-n	kεl ke la	voˈra-n

they.F= do.FUT.3-F.PL that that they.F= want.FUT.3-F.PL

Mesolcinese has lost inversion.

the verbal head can still agree with a nearby NP in number and gender, but should lose the ability to agree in person. Such instances of verbal agreement would be adjectivelike in this respect. (Baker 2008: 85-86;emphasis mine) In the light of Baker's quote, I suggest that, after the original person/number ending -n was lost in Mesolcinese, finite verbs at the third person began to undergo morphophonological agreement, like adjectives and participles. This pattern would be impossible in a language like Bregagliotto, which exhibits a solid mechanism of person agreement: recall that, in Bregagliotto, the PLURALISER ^n is merged with person probes and is barred when T is valued as 1 st /2 nd person because 1 st /2 nd person cannot be pluralised (cf. §3). In Mesolcinese, conversely, n is free to combine with verbs at any person because n has become a morpho-phonological marker that can be attached to any inflected element within the Spell-Out domain of feminine plural clitics. Hence, when verbs at the 1 st /2 nd person are c-commanded by a feminine plural clitic, the morphophonological marker -n is attached to the verb after the 1 st /2 nd person ending (the relevant example is repeated below):

(33) la ˈtʃam-i-əŋ (Mes.) them.F= call-1SG-FPL 'I call them.F'

In conclusion, the hypothesis that plural +n in Mesolcinese instantiates morphophonological agreement accounts for various peculiarities of Mesolcinese, noticeably why finite verbs agree in gender and with object clitics (two properties that, in the other (Italo)Romance varieties characterise past participles).

The fact that the Mesolcinese +n became a morphophonological marker of number/gender agreement after the person/number element -n had been lost supports the view that subject to morpho-phonological, participle-like agreement: as a result, inflected verbs in Mesolcinese are combined with +n when they are in the c-command domain of feminine plural subject and/or object clitics.


A Durif

⁎⁎ M Richou

G Kermouche

J.-M Bergheau

Inverse identification of tungsten static recrystallization kinetics under high thermal flux

Understanding of recrystallization phenomenon is essential to apprehend damage process of tungsten armored plasma facing components and to optimize their use in tokamak environment. In ITER, plasma facing compo-nents will reach extreme surface temperature value up to 2000 °C. Up to now, recrystallization kinetics of ITER tungsten grade were investigated from 1150 °C to 1350 °C. In order to understand tungsten recrystallization process on the wider relevant temperature range, kinetics have to be investigated at higher temperature and on several tungsten grades. Usually, kinetics are investigated by performing successive isothermal annealings on tungsten samples. Due to number of ITER tungsten grades and large temperature range (from 500 °C to 2000 °C), an important amount of tungsten samples have to be prepared to investigate recrystallization kinetics on ITER representative conditions. In this paper, an innovative way is proposed to obtain recrystallization kinetics of ITER tungsten grade based on the use of small-scale plasma facing component tested under high heat flux. Thanks to the use of this inverse method, tungsten recrystallization kinetics are identified at 1348 °C ± 29 , 1480 °C ± 29 , 1586 °C ± 28 and 1696 °C ± 27 by using experimental measurements and Johnson-Mehl-Avrami-Kolmogorov model. Then, obtained kinetics are used as input data in numerical post-treatments to obtain tungsten recrystallization gradients after 500 thermal cycles at 20 MW/m 2 .

Introduction

For the ITER divertor, plasma facing components are made with tungsten as armor material, bonded on a copper alloy tube as heat sink structural material and cooled by water. Such components withstand high heat flux up to 20 MW/m 2 and consequently satisfy ITER requirements [START_REF] Ezato | Progress of ITER full tungsten divertor technology qualification in Japan[END_REF][START_REF] Pintsuk | Characterization of ITER tungsten qualification mock-ups exposed to high cyclic thermal loads[END_REF][START_REF] Hirai | Status of technology R&D for the ITER tungsten divertor monoblock[END_REF][START_REF] Hirai | Use of tungsten material for the ITER divertor[END_REF][START_REF] Gavila | High heat flux testing of mock-ups for a full tungsten ITER divertor[END_REF][START_REF] Riccardi | Preliminary results of the experimental study of PFCs exposure to ELMs-like transient loads followed by high heat flux thermal fatigue[END_REF]. However, due to high heat flux, the loaded surface reaches extreme temperature values up to 2000 °C and strong thermal temperature gradient is generated on a thickness in the range of 6 mm [START_REF] Li | Interpretation of the deep cracking phenomenon of tungsten monoblock targets observed in high-heat-flux fatigue tests at 20 MW/m2[END_REF][START_REF] Panayotis | Fracture modes of ITER tungsten divertor monoblock under stationary thermal loads[END_REF]. 2000 °C is large enough to alter tungsten microstructure by recrystallization. Understanding of recrystallization phenomenon is essential to apprehend damage process of such components and to optimize their use in tokamak environment. Hereafter, this means tungsten recrystallization kinetics have to be investigated. Up to now, kinetics were obtained by isothermal annealings on one tungsten grade relevant with ITER specifications (called here abusively ITER tungsten grade) on a restricted temperature range from 1150 °C to 1350 °C [START_REF] Lopez | Thermal stability of warmrolled tungsten[END_REF]. To fulfill the gap and then understand tungsten recrystallization phenomenon on the entire temperature range, an innovative way is proposed in this paper. Based on the use of small-scale plasma facing component tested under high heat flux, this inverse approach aims to benefit from thermal temperature gradient generated experimentally to obtain tungsten recrystallization kinetics.

In the first part of this paper, inverse methodology is described. Second, based on hardness measurements, tungsten recrystallization kinetics are identified thanks to Johnson-Mehl-Avrami-Kolmogorov model (JMAK) [START_REF] Humphreys | Recrystallization and Related Annealing Phenomena[END_REF]. Then, numerical integration of obtained kinetics highlights that consistent tungsten recrystallization gradients are obtained.

Assumptions

= X b t t 1 exp( ( ) ) n n inc (1)
JMAK model (equation ( 1)) can be used to describe the recrystallized fraction (X) evolution of material over the annealing time ⁎⁎ Principal corresponding author. ⁎ Corresponding author.

E-mail addresses: alan.durif@cea.fr (A. Durif), marianne.richou@cea.fr (M. Richou).

T [START_REF] Humphreys | Recrystallization and Related Annealing Phenomena[END_REF]. tinc is representing the incubation time, to take into account recovery phase before recrystallization [START_REF] Humphreys | Recrystallization and Related Annealing Phenomena[END_REF], n is the Avrami exponent set at 1.098 [START_REF] Lopez | Thermal stability of warmrolled tungsten[END_REF] and b is thermo-dependent parameter. Recrystallization is a thermally activated process. Relationships between JMAK parameters and annealing temperature over temperature range are usually decribed by Arrhenius laws [START_REF] Humphreys | Recrystallization and Related Annealing Phenomena[END_REF][START_REF] Lopez | Thermal stability of warmrolled tungsten[END_REF]. In this way, inverse approach aims to propose a method to estimate parameters b and tinc at specific annealing temperatures and aim to identify Arrhenius relationships for these both parameters on a large temperature range. For that, X has to be estimated over different annealing times per annealing temperature.

= X HV HV HV HV in in rx (2)
According to equation (2) [START_REF] Lopez | Thermal stability of warmrolled tungsten[END_REF][START_REF] Baral | In situ characterization of AA1050 recrystallization kinetics using high temperature nanoindentation testing[END_REF], X can be estimated from hardness measurements, with HV the measured hardness after any annealing time at a specific annealing temperature, HV rx the measured hardness on fully recrystallized material and HV in the measured hardness on initial material. Indents are performed at CEA Cadarache (IRFM) using a load of 10 kg and a dwell time of 10 s [START_REF] Lopez | Thermal stability of warmrolled tungsten[END_REF].

In this way, based on the use of small-scale plasma facing component tested under high heat flux, inverse approach aims to benefit from thermal temperature gradient obtained experimentally. Hardness at specific positions, corresponding to a loaded annealing temperature are performed. Annealing temperatures are identified thanks to use of the thermal temperature gradient obtained numerically. Measured hardness related to same annealing temperature per block are averaged and then converted in X (Eq. ( 2)).

To obtain parameters from Eq. ( 1), each X obtained is assigned to an equivalent annealing time (t annealing ). t annealing per investigated block is defined as a function of number of loaded cycles (N cycle ) and steady state loaded time (Δt) (Eq. ( 3)). Parameters b and tinc are then identified per investigated annealing temperature thanks to the use of least squares method regarding Eq. ( 1) and Arrhenius laws fitting. Finally, Arrhenius relationships are used as input data in numerical anisothermal JMAK post treatment to model tungsten recrystallization gradient after 500 thermal cycles at 20 MW/m 2 . Anisothermal JMAK model is commonly used in literature for anisothermal paths [START_REF] Bergheau | Finite Element Simulation of Heat Transfer[END_REF].

= t N t * annealing cycle (3)

Material and method

Materials

In preparation of the actively cooled divertor of WEST tokamak -1000 cycles at 10 MW/m 2 followed by 300 cycles at 20 MW/m 2 for M4

-1000 cycles at 10 MW/m 2 followed by 500 cycles at 20 MW/m 2 for M5.

For thermal loading at 10 MW/m 2 (in total 10 000s), tungsten reaches maximum temperature close to 1000 °C being not enough to have an impact on tungsten microstructure [START_REF] Lopez | Thermal stability of warmrolled tungsten[END_REF].

Finite elements modeling

Inverse approach aims to benefit from thermal temperature gradient observed under 20 MW/m 2 to obtain tungsten recrystallization kinetics. For that, temperature gradient and equivalent annealing time over cycles is estimated using numerical simulation performed on finite elements code (ANSYS 17.2).

Numerical model presented in Fig. 1 (a), is representative to studied tungsten blocks M4 and M5. Thanks to the use of symmetry planes only quarter part of block is modeled taking into account the presence of 1*1 mm 2 chamfer in the modeling. 38376 quadratic elements are used to mesh the 3D geometry. Heat conductivity and coefficient of thermal expansion used are those presented for tungsten, Cu-OFHC and CuCrZr in [START_REF] Li | Interpretation of the deep cracking phenomenon of tungsten monoblock targets observed in high-heat-flux fatigue tests at 20 MW/m2[END_REF]. In this study, 20 MW/m 2 heat flux is applied on the upper surface and CEA routine [START_REF] Schlosser | Finite elements calculations for plasma facing components[END_REF] is used to calculate heat transfer coefficients (T°=22 °C, = v 10 m/s and p = 2.25 MPa) due to water cooling during high heat flux tests at the inner wall pipe. Fig. 1(b), highlights that thermal loadings at 20 MW/m 2 involve strong thermal temperature gradient leading to extreme temperature values from 1810 °C at the loaded surface to 902 °C 4 mm in the depth of the block.

Maximum surface temperature obtained is compared to that measured by infrared camera during the experimental campaign [13] and revealed that numerical model estimates consistent thermal results. This map is used for the identification of positions related to specific annealing temperature.

Annealing time

t annealing (equation ( 3)) has to be estimated for each studied block. Fig. 2 (a) shows the temperature evolution (over one thermal cycle) of two nodes placed on both sides of annealing temperature range explored. Steady state is obtained after 5s heating. Consequently, conservative study should be achieved assuming Δt = 5 s. However, considering Δt = 5 s in this study, involves that heating phase (from 0 s to 5 s heating) is neglected. To evaluate the impact of this assumption, kinetics will be investigated assuming two different t annealing per block (Table 1) with Δt = 5 s which involved shorter time to obtain fully recrystallized material (conservative study) and Δt = 10 s which assumed that entire heating phase play a role in the microstructure change. 2. Due to a deteriorated surface of block M5, no indent is performed for positions related to annealing temperature equal to 1586 °C and 1696 °C (see Fig. 1 for global thermal gradient). Moreover, indents measure approximately 200 μm diagonal which involve vertical thermal temperature gradient in the order of 50 °C. Temperature assigned for each indent is consequently given with an uncertainty of ± 25 °C. Hardness values are then averaged over 3 indents within a same loaded temperature (Fig. 2,c). The maximum horizontal temperature variation over indents varying from ± 4 °C at 2.6 mm depth to ± 2 °C at 0.6 mm depth which involves a maximum final uncertainty of ± 29 °C on the average temperature estimated for each investigated zones (Fig. 2c).

Results and discussion

Hardness measurements

To estimate HV in , 20 indents are performed on tungsten plate (28*28*12mm 3 ) supplied by Advance Technology and Materials (AT& M). Average hardness (HV in ) obtained (458 HV 10 ± 2) is compared with average hardness obtained from indents performed far from the M4 loaded surface (451 HV 10 ± 5) revealing that material supplied can be used to estimate HV rx . Isothermal annealing at 1250 °C (96 h) is achieved on tungsten sample (9*12*3 mm 3 ) obtained from surface tungsten plate to estimate HV rx . 20 indents are performed on the sample after annealing. Average hardness (HV rx ) obtained is equal to 378 HV 10 ± 2. Based on HV in (458 HV 10 ± 2) and HV rx (378 HV 10 ± 2) each hardness values obtained for blocks M4 and M5 are converted in X thanks to equation (2) (Table 2).

Indents are also performed at 8.1mm from the edge of block M5 in order to valid the inverse method on another part of the block. Due to thermal gradient, 5 hardness measurements are performed over the depth. Consequently, hardness is not averaged and error bars presented Fig. 4 (b) are representative to statistic obtained for HV in ( ± 2).

Recrystallization kinetics by inverse method

At annealing temperatures equal to 1586 °C and 1696 °C only one X is provided which corresponds to measurements performed on M4. To provide another point for the determination of these kinetics, one assumption is made for the determination of X related to the block loaded at 500 cycles (M5). In any case, the X related to M5 for a given annealing temperature is higher than the one obtained for same annealing temperature on M4. At 1696 °C, X is fixed at 100%. Parameters b and tinc are obtained per annealing temperature by fitting equation (1) using least squares method (Table 3) for both given annealing times. Related recrystallization kinetics obtained for each annealing temperature (assuming Δt = 5 s) and Arrhenius laws are given in Fig. 3. Arrhenius straight as the method imposes it (R 2 =0.9999).

Discussion

Fig. 4 (a) shows tungsten recrystallization gradient obtained numerically after 500 cycles at 20 MW/m 2 using determinated kinetics at 3.5mm from the edge assuming Δt = 5 s and Δt = 10s. Average measurements obtained at 3.5mm from the edge of blocks are used to fit kinetics parameters. Consequently, Fig. 4 (a) shows consistent evolution of tungsten recrystallized fraction with regard to experimental data (20 MW/m 2 ) X (%) 13 ± 7 71 ± 14 91 ± 12 98 ± 8 displayed Table 2. It shows also that the realistic annealing time is between Δt = 5 s and Δt = 10s. Fig. 4 (b) highlights recrystallized fraction evolution over the block depth at 8.1mm from the edge. It shows consistent predictions of X tendency.

In this paper, two tungsten blocks are used to fit tungsten recrystallization kinetics. In further studies, number of investigated blocks could be increased in order to optimize the fitting procedure and provide more consistent data. Also, to increase statistics and minimize temperature uncertainty per investigated kinetic, micro-indents could be considered.

Conclusion

This paper proposes an innovative way to investigate tungsten recrystallization kinetics used as armored material in plasma facing components. Here above, kinetics were obtained at 1348 °C ± 29 , 1480 °C ± 29 , 1586 °C ± 28 and 1696 °C ± 27 . JMAK parameters (b and tinc) obtained are extrapolated over the explored temperature range using Arrhenius relationships. To finish, these are used as input data in numerical post-treatments and consistent tungsten recrystallization gradients are obtained.

(PHASE 2 )

 2 , mock-ups were manufactured. Composed of 7 tungsten blocks supplied from Advance Technology and Materials, these were bonded on Cu-OFHC interlayer (1 mm) finally bonded on a copper alloy tube (CuCrZr) used as heat sink structural material[13]. Tungsten block dimension is 27.4 mm (width) * 26 mm (height) * 12 mm (depth). The minimum distance from tungsten upper surface to the copper interlayer is 6 mm. Tube inner diameter is 12 mm, while the outer diameter of the tube is 15mm. These mock-ups were exposed to electron beam JUDITH 1 at Forschungszentrum Julich[13]. In this paper, two tungsten blocks (M4 and M5) from one mock-up named M2-2 in [13] are investigated. These were exposed to cyclic high heat flux (10s ON / 10s OFF):

Fig. 1 .

 1 Fig. 1. a) Numerical modeling, b) Thermal temperature gradient obtained under 20 MW/m 2 .

Fig. 2 (

 2 Fig. 2(b) shows indents performed on the external surface of block M4 and zoom Fig. 2(c) displays hardness values for each indents. Zoom highlights that hardness increases by the depth. Similar measurements are performed on block M5. Average hardness values obtained for blocks M4 and M5 are presented in Table2. Due to a deteriorated surface of block M5, no indent is performed for positions related to annealing temperature equal to 1586 °C and 1696 °C (see Fig.1for global thermal gradient). Moreover, indents measure approximately 200 μm diagonal which involve vertical thermal temperature gradient in the order of 50 °C. Temperature assigned for each indent is consequently given with an uncertainty of ± 25 °C. Hardness values are then averaged over 3 indents within a same loaded temperature (Fig.2, c). The maximum horizontal temperature variation over indents varying from ± 4 °C at 2.6 mm depth to ± 2 °C at 0.6 mm depth which involves a maximum final uncertainty of ± 29 °C on the average temperature estimated for each investigated zones (Fig.2c).To estimate HV in , 20 indents are performed on tungsten plate (28*28*12mm 3 ) supplied by Advance Technology and Materials (AT& M). Average hardness (HV in ) obtained (458 HV 10 ± 2) is compared with average hardness obtained from indents performed far from the M4 loaded surface (451 HV 10 ± 5) revealing that material supplied can

Fig. 2 .

 2 Fig. 2. a) Temperature evolution of two nodes, b) indents performed on M4 are assigned to temperature, c) hardness values obtained for M4 and related annealing temperature.

Fig. 3 .

 3 Fig. 3. a) Recrystallization kinetics obtained by inverse method and b) related Arrhenius relationships assuming Δt = 5 s.

Fig. 4 .

 4 Fig. 4. Evolution of the recrystallized fraction obtained numerically for both annealing times assumed (5s and 10s) and comparison with experiments performed at: a) 3.5mm from the edge of the block, b) 8.1mm from the edge of the block.

Table 1

 1 Equivalent annealing time assumed per block

		M4 (300 cycles)	M5 (500 cycles)
	Δt = 5 s	1500 s	2500 s
	Δt = 10 s	3000 s	5000 s

Table 2

 2 Average hardness values and related recrystallized fraction obtained

		T(°C)	1348 ± 29	1480 ± 29	1586 ± 28	1696 ± 27
	500 cycles	Hv 10	425 ± 8	399 ± 3	-	-
	(20 MW/m 2 )	X (%)	41 ± 10	73 ± 4	-	100
	300 cycles	Hv 10	448 ± 5	401 ± 12	385 ± 10	380 ± 6

Table 3

 3 JMAK parameters identified for two annealing times using least squares method

	b

Acknowledgments

This work has received CEA funding from the "Programme Transverse de Compétence, Matériaux et Procédés (PTC-MP). This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training program 2014-2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.


Introduction: motivations

Labels as instruments for financing AECPG provision «Instrument […] that […] regulates the presentation of product-specific information to consumers. This information might describe use characteristics of the product, such as price, taste, and nutrition, or nonuse characteristics, such as the environmental impact or moral/ethical elements surrounding the product's manufacturing process» [START_REF] Teisl | The economics of labeling : an overview of issues for health and environmental disclosure[END_REF].

 A label reduces asymmetric information, a source of market failure.

 Consumers express their preferences for environmental quality through their food choices (demand for AECPG).

 Farmers are encouraged to adopt environmentally-friendly agricultural practices (supply of AECPG).

Information on the environmental impact of the food product.

Ecolabel

Willingness to pay for AECPG [START_REF] Moon | Willingness to pay for environmental practices: implications for ecolabeling[END_REF].

Willingness to accept for providing environmental services.

p. 4

Titre de la présentation Date / information / nom de l'auteur Literature review  Assumption on consumers behaviour:

 Each consumer buys the product until the benefit he/she gets from 1 extra-unit equals its marginal cost.

 Allocation of goods through the market:

 Private good: benefits from consumption are individual. Rationality leads to the optimal allocation.

 Public good: the benefits from each unit provided are for everyone. By only considering his/her individual benefit from purchasing one more unit, a rational consumer does not take into account the benefits to others [START_REF] Cornes | Easy riders, joint production, and public goods[END_REF]. The allocation is not optimal.

 A voluntary contribution through the market does not meet the Bowen-Lindahl-Samuelson (BLS) condition for the optimal provision of a PG [START_REF] Sandmo | Public Goods[END_REF]:

 The sum of the marginal willingness to pay for the PG of all the beneficiaries should be equal to the marginal cost of production.

 Public economics theory on the voluntary contribution to public goods (PG) provision :

 Environmental quality is underfunded. Ecolabels are inefficient tools.

Labels as instruments for financing AECPG provision p. 5

Titre de la présentation Date / information / nom de l'auteur

Literature review  Empirical studies on other labels in the « green market » :

 Emerging labels emphasising the nutritional/sanitary quality of food produced with environmentally-friendly practices (0 pesticides, 0 GMO, 0 hormones, 0 antibiotics).

 Organic label (strict limitation of synthetic chemical inputs use): health concerns are the primary cause of purchase [START_REF] Hughner | Who are organic food consumers? A compilation and review of why people purchase organic food[END_REF][START_REF] Kushwah | Ethical consumption intentions and choice behavior towards organic food. Moderation role of buying and environmental concerns[END_REF][START_REF] Loureiro | Assessing consumer preferences for organic, eco-labeled, and regular apples[END_REF].

 Internalities from food consumption :

 Asymmetric information on the costs and benefits "borne by individuals themselves in the future but are ignored at the point of consumption" : balanced diet, addictions, risk of developing cancer or cardio-vascular diseases... [START_REF] Griffith | Corrective taxation and internalities from food consumption[END_REF].

Labels as instruments for financing AECPG provision

Hypothesis: «environment and health» labels would capture both the willingness to pay of consumers with environmental concerns and the willingness to pay of consumers with health concerns, what should increase the level of AECPG provision in comparison with ecolabels.

p. 6

Titre de la présentation Date / information / nom de l'auteur

Literature review

 Numerous empirical studies on stated or observed choices between conventional products and products with a lower environmental impact [START_REF] Bougherara | Eco-labelled food products: What are consumers paying for?[END_REF], particularly using discrete choice modelling (Bjorner et al, 2004;[START_REF] Lusk | Public preferences and private choices: effect of altruism and free riding on demand for environmentally certified pork[END_REF][START_REF] Brécard | Determinants of demand for green products: an application to eco-label demand for fish in Europe[END_REF][START_REF] Brécard | Consumer preferences for eco, health and fair trade labels. An application to seafood product in France[END_REF].

 Theoretical modelling: impure public good model (Cornes and Sandler, 1994).

 Consumers' utility is derived from the characteristics of the goods they consume [START_REF] Lancaster | A new approach to consumer theory[END_REF].

 Impure public good:

• Private good for which the production is joint to the delivery of a PG.

• Display a private characteristic and a public characteristic.

 Kötchen (2005Kötchen ( , 2006) ) : theory of green consumption. A consumer allocates her/his income among:

• An impure public good 𝑔 (eco-labeled product) with the private characteristic 𝑋 and the public characteristic 𝑌.

• Its conventional substitute 𝑐, a private good with the private characteristic 𝑋.

Modelling consumption choices p. 7  Show the effect on the level of 𝒀 of the information available to consumers on the complementary provision of 𝑯 and 𝒀.

p. 8

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 BBC Label (France):

Enriching dairy cows' diet with grass fodders and extruded linseed [START_REF] Weill | Method to evaluate the quantity of methane produced by a dairy ruminant and method for decreasing and controlling this quantity[END_REF]:

 Increases the omega-3 content of milk.

 Decreases enteric methane emissions per litre of milk.

Illustrative example

BBC label (since 2000):

Approximately 400 dairy farmers.

X: milk Y: climate change mitigation H: omega-3 intake p. 9

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Main theoretical findings

When environmentally-friendly practices produce a good with benefits for health:

 The environmental and health labelling of the product increases the provision of AECPG compared with a health label or an eco-label.

 The level of the increase depends on consumers preferences for the food product, health and environmental issues, and on the market size.

 Health concerns indirectly contribute to financing AECPG provision and, under certain conditions, up to the optimal level of an environmental agency. Eco-label (Kötchen, 2005(Kötchen, , 2006) ) Comparison of the provision levels of AECPG p. 18

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Discussion

When environmentally-friendly practices produce a good with benefits for health (complementary provision of AECPG and a positive consumption internality):

 The environmental and health labelling of the product increases the provision of AECPG compared with a health label or an eco-label.

 The level of the increase depends on the relative preferences for the food product, health and environmental issues, and on the market size.

 Health concerns indirectly contribute to financing AECPG provision and, under certain conditions, up to the optimal level of an environmental agency.

Main findings p. 19

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Discussion

Limits of the theoretical model  Assumption that 𝒑 𝒈 is identical under the 3 types of labelling.

 Transaction costs (information, certification) would affect their relative performances.

 Assumption that consumers are homogeneous with homothetic preferences (no income effect).

 There exist different groups of consumers depending on preferences and income levels:

 Young altruistic individuals with high levels of revenue, education and environmental awareness exhibit high preferences for environmental quality [START_REF] Aldanondo-Ochoa | The private provision of public environment: consumer preferences for organic production systems[END_REF][START_REF] Brécard | Determinants of demand for green products: an application to eco-label demand for fish in Europe[END_REF][START_REF] Lusk | Public preferences and private choices: effect of altruism and free riding on demand for environmentally certified pork[END_REF][START_REF] Moon | Willingness to pay for environmental practices: implications for ecolabeling[END_REF].

 Older individuals with a lower level of education exhibit high preferences for health [START_REF] Brécard | Consumer preferences for eco, health and fair trade labels. An application to seafood product in France[END_REF][START_REF] Govindasamy | Predicting willingness-to-pay a premium for organically grown fresh produce[END_REF][START_REF] Schifferstein | Health-related determinants of organic food consumption in the Netherlands[END_REF].

p. 20

Titre de la présentation Date / information / nom de l'auteur  This theoretical analysis contributes to:

 Better understand the market paramaters influencing the impact of food labelling on AECPG provision.  Discussing the development of « environment and health » labels as a lever to reach EU's environmental and climate targets as part of the « Farm to Fork » strategy.

 Recommendations for public policies:

 Health labelling is relevant to increase AECPG provision through the market.

 Bring to light complementarities between positive consumption internalities and PG provision in the agricultural sector requires investing in research and education.

Conclusion

p. 21



  Impure public good (labeled product): 𝑔 (price 𝑝 𝑔 )  Its conventional substitute: 𝑐 (price 𝑝 𝑐 )  Private characteristic (food): 𝑋 𝑖 = 𝑐 𝑖 + 𝑔 𝑖  Public characteristic (global AECPG) : 𝑌 = 𝑌 𝑖 + 𝑌 -𝑖 , 𝑌 𝑖 = 𝛽𝑔 𝑖  Private characteristic (health): 𝑯 𝒊 = 𝜶𝒈 𝒊  Joint production technology: 1 unit of 𝑔 provides 𝜶 units of 𝐻 et 𝜷 units of 𝑌.  Assumption for the viability of 𝑐 on the market : 𝑝 𝑔 > 𝑝 𝑐  Preferences: 𝒎𝒂𝒙 𝒄 𝒊 ,𝒈 𝒊 𝑼 𝒊 𝑿 𝒊 , 𝑯 𝒊 , 𝒀  𝑰 homogeneous consumers with income 𝑟. p. 11 Titre de la présentation Date / information / nom de l'auteurTheoretical modelConsumers have no information on the health characteristic of good 𝑔. No demand for characteristic 𝐻.

  𝑖 , 𝑌, 𝐻 𝑖 | 𝑖 𝑋 𝑖 = 𝑐 𝑧 𝑐 + 𝑔 1 -𝑧 𝑐 , 𝑌 = 𝛽𝑔 1 -𝑧 𝑐 , 𝑖 , 𝑌, 𝐻 𝑖 | 𝑖 𝑋 𝑖 = 𝑐 𝑧 𝑐 + 𝑔 1 -𝑧 𝑐 , 𝑌 = 𝛽𝑔 1 -𝑧 𝑐

Assumption:

  𝑈 𝑖 𝑋 𝑖 , 𝑌, 𝐻 𝑖 = 𝑎 ln 𝑋 𝑖 + 𝑏 ln 𝑌 + 𝑐 ln 𝐻 𝑖  A health label reaches the objective of the environmental agency if An environment and health label reaches the objective of the environmental agency if

  𝑋 𝑖 = 𝑐 𝑖 + 𝑔 𝑖 , 𝑯 𝒊 = 𝜶𝒈 𝒊 , 𝒀 𝒊 = 𝜷𝒈 𝒊 , 𝒀 = 𝒀 𝒊 + 𝒀 -𝒊 , 𝑝 𝑐 𝑐 𝑖 + 𝑝 𝑔 𝑔 𝑖 ≤ 𝑟 𝑈 𝑖 𝑋 𝑖 , 𝑌, 𝐻 𝑖 = 𝑎 ln 𝑋 𝑖 + 𝑏 ln 𝑌 + 𝑐 ln 𝐻 𝑖

	max 𝑐 𝑖 ,𝑔 𝑖 max 𝑈 𝑖 𝑋 𝑖 , 𝑌, 𝐻 𝑖 | 𝑋 𝑖 ,𝐻 𝑖 Environment and health label 𝟏 𝒀 𝒆 = 𝟏 𝜷 𝒑 𝒈 -𝒑 𝒄 𝒓 𝟏 𝑰 + 𝒂 𝒃 𝑋 Health label 𝟏 𝒀 𝒉 = 𝟏 𝜷 𝒑 𝒈 -𝒑 𝒄 𝒓 ( 𝟏 𝑰 + 𝒂 𝑰𝒄 )
	𝟏 𝒀 𝒆𝒉	=	𝟏 𝜷	𝒑 𝒈 -𝒑 𝒄 𝒓	(	𝟏 𝑰	+	𝒂 𝒃 + 𝑰𝒄	)

𝑖 = 𝑐 𝑖 + 𝑔 𝑖 , 𝒀 𝒊 = 𝜷𝒈 𝒊 , 𝒀 = 𝒀 𝒊 + 𝒀 -𝒊 , 𝑝 𝑐 𝑐 𝑖 + 𝑝 𝑔 𝑔 𝑖 ≤ 𝑟 p. 12 Titre de la présentation Date / information / nom de l'auteur Theoretical model Consumers have no information on the environmental characteristic of good 𝑔.  No demand for characteristic 𝑌. 𝑈 𝑖 𝑋 𝑖 , 𝑌, 𝐻 𝑖 | 𝑋 𝑖 = 𝑐 𝑖 + 𝑔 𝑖 , 𝑯 𝒊 = 𝜶𝒈 𝒊 , 𝑝 𝑐 𝑐 𝑖 + 𝑝 𝑔 𝑔 𝑖 ≤ 𝑟  Consumers are not informed of the provision of 𝑌 but the AECPG is still provided through the joint agricultural production technology 𝒀 = 𝜷𝒈 𝒊 + 𝒀 -𝒊 p. 13 Titre de la présentation Date / information / nom de l'auteur Theoretical model max 𝑋 𝑖 ,𝐻 𝑖 ,𝑌 𝑈 𝑖 𝑋 𝑖 , 𝐻 𝑖 , 𝑌 | Consumers have a complete information on the characteristics of good 𝑔. p. 14 Titre de la présentation Date / information / nom de l'auteur

Results

Assumption :

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