Pablo Kirtchuk

come

1 Cf. initial /q u-/ in Latin and its cognates in IE, which mark both interrogative and indefinite morphemesand negative ones too, in certain contexts. Another Hebrew and indeed Semitic morpheme whose functions are somewhat analogous to those of that IE morpheme is /ej/.

Here is a list of minimal pairs in CH created following the emergence of tones thus confirming Hombert 1975 (the first row represents BH variants, the second CH ones) : 'taar tar 2 tar 'barber's knife' 3 tar 'turn around; visit'

Biblical Hebrew Contemporary Hebrew // = [] [Ø] + [] (+ []) // = [] [Ø] + [] /w/ = [w] [v] /b/ = [b] + [β] [b] (+ [v]) /t/ = [T] + [θ] [t] /T/ = [T] [t] // = [] + [s] [s] /s/ = [s] [s] /K/ = [K] + [χ] [k] + [x] /q/ = [q] [k] /å/ = [å] [a] /a/ = [a

Morphology

In terms of classical morphological typology à la Humboldt and Sapir (1921), Hebrew is an inflecting language. Moreover, morphology is probably its most enduring structure, bearing an unequivocal Semitic stamp. Yet a typological difference that distinguishes CH from BH and MH relates to composition and prefixation. BH exhibits practically no example of composition -all nouns are construed by derivation and can be expanded by means of the construct-state. CH, on the other hand, has a number of compound nouns and a score of nominal prefixes, mostly spatio-temporal and quantitative [START_REF] Kirtchuk | Renouvellement grammatical, renouvellement lexical et renouvellement conceptuel en Sémitique[END_REF]. Neither stage has verbal composition, while in IE languages pre-verbs of prepositional and ultimately nominal origin are common (e.g. ex-, in-, trans-, de-, re-… -port). As in all Semitic languages, the core morphology consists of an inventory of lexical morphemes called roots and of grammatical morphemes or patterns called schemata, whereby roots are actualized into word forms. Each root has an overall sense with a concrete meaning and often also an abstract, metaphoric one, sometimes resulting in polysemy. As long as the root is not interwoven into a schema it has no existence in discourse. The original Semitic root is bi-phonemic [START_REF] Bohas | Une théorie de l'organisation du lexique des langues sémitiques , Matrices et étymons[END_REF][START_REF] Lyon | Hebrew as a Case-Test for the 2-Phoneme Root in Semitic[END_REF][START_REF] Kirtchuk | LUIT: Language -a Unified and Integrative Theory[END_REF] though for practical reasons it is represented here as being tri-phonemic. This distinction is important, for not taking it in account obliterates the strong iconic (semantic cum formal) stamp that characterizes what I have called root-grapes, namely the threephoneme groups which gravitate around a single bi-phonemic one, being its expansions. The schemata constitute frames that include vocalic and often consonantal components with which the roots are interwoven. Most schemata have a grammatical morphemic role, and that is the case mainly in the verbal system, in which they allow to distinguish diathesis and aspect. Thus, in the basic form of the verb, BH has R 1 åR 2 aR 3 and R 1 u:R 2 aR 3 (respectively 3p.m.sg.pf active and passive), in the intensive form R 1 iR 2 R 2 e:R 3 and R 1 uR 2 R 2 aR 3 , and in the factitive/causative form of the verb it has hiR 1 R 2 iR 3 and hoR 1 R 2 aR 3 . The expression of diathesis by vocalic change is a constant feature of Hebrew morphology through the ages, the only caveat being relevant to CBH: the niR 1 R 2 aR 3 pattern serves as a substitute for R 1 u:R 2 aR 3 as the passive of the basic or Qal form. The total number of available schemata -verbal, nominal, and in a much smaller measure, of other categories, is of around a hundred. Demonstrative deictics are composed of the elements /,h,l,z/ or combinations thereof. Autonomous personal dialogic deictics are founded on the theme /an-/. The non-person, to use [START_REF] Benveniste | Structure des relations de personne dans le verbe[END_REF] term, is expressed, like in other languages, by the application of a demonstrative deictic to animates (the result is traditionally called 'third person pronoun'). As in other languages [START_REF] Kirtchuk | /et/ ou ne pas /et/: l'actant Y en hébreu et au-delà[END_REF], even in Hebrew, a non-compounding language, deictics are capable of composition; thus CBH has /ha(l)-lå-ze/ and /ha(l)-lå-zu/ (sic), two emphatic sg.m./f. demonstratives composed of three distinct deictic elements (for the differences between prototypical deictics and nouns, and thus between monstration and conceptualization, cf. [START_REF] Kirtchuk | LUIT: Language -a Unified and Integrative Theory[END_REF]. Other elements not founded upon lexical roots are indefinites-interrogatives, some conjunctions and some prepositions. As in many languages, many prepositions are of nominal origin. CBH is a synthetic language with a large number of inflectional processes comprising morphological marking of the major grammatical categories on both the noun and the verb. The noun inflects for gender and number, and there is a semi-productive inflection for the directive case. The verb inflects for person (including gender and number) and for aspect. The marked gender for both verb and noun is the feminine, as in all languages which exhibit a sex-based gender distinction. The number distinction in the noun is threefold: singular, plural and dual. The only adjectival scheme morphologically marked as such is the one denoting affiliation to a group, derived by suffixation of /-ij/ to proper names of peoples, places and the like. Many concepts usually encoded by adjectives in Indo-European languages are expressed in CBH by stative verbs marked as such by their specific morphology. BH has a limited number of adverbs formed by a noun and an erstwhile accusative, which we shall more appropriately call an ad-verbal stressed case suffix /-åm#/: /jomåm/ 'at daytime' (< /jo:m/ 'day'), /dumåm/ 'silently' (< /do:m/ 'silence'), /innåm/ 'gratis' (< /en(n)/ 'grace'), /rejqåm/ 'vacuously' (< /rejq/ 'empty'), /åmnåm/ 'indeed' (< /åme:n/ 'truth'), /pito:m/ 'suddenly' (< /pεta/ 'sudden'). /šilšo:m/ 'the day before yesterday' does not seem to belong here. In any case, this is a close list whose members function in IH too. The mechanism, however, is obsolete including in BH itself. On the other hand, a mechanism which is productive throughout the history of Hebrew to this day, consists of the so-called he locale which is in fact a directive suffix, an enclitic /-å#/ postposed to the noun, probably akin to adverbal /-åm#/ (though evidence from Ugaritic might plead for a consonantal /h/ origin). Thus, we have in BH, e.g., /negbå/ 'southwards from /nεgεb/ 'south' and in IH, e.g., /håirå/ 'towards the city' from /ha-ir/ 'the-city'. In MH, the impact of analogy is extensively attested: thus, the conjugation of roots with R 2 = w/j and that of those with R 3 =  merge in favour of the former so as to yield, for the root mc -of frequent use as a quotation formula -the first person plural past tense form /måci:nu/ 'we found' instead of the classical one /måcånu/ 'id.'. Modal forms which are rare in CBH disappear altogether. Other important morphological evolutions typical of MH are: the influence of the nipal scheme on hitpae:l yielding the reflexive form nitpaal, the total disappearance of pual (save in the participle), the proliferation, again through Aramaic influence, of the Akkadian factitive/causative šape:l (which reflects the sibilant characteristic of this language in correspondance to Semitic grammatical /#h-/) and of the reflexive ettapal. The nipal and pie:l patterns acquire an aditional inchoative meaning. Specific and rare forms found in CBH such as those of the imperfect jussive and cohortative as well as the archaic personal suffix /-ki/ for the 2nd person feminine singular disappear altogether, due to simplification of the morphology through analogy and syntactic re-organization of the verbal system. The autonomous deictic for the first person singular is  a ni, while CBH  a noki disappears almost completely. The same holds for the plural, in which ånu: replaces  a nanu: Under Aramaic influence, att is used along with attå as the second person singular masculine. As a whole, BH syntax is rather synthetic and paratactic whereas MH is rather analytic and hypotactic (which renders IH closer to the latter in both respects). Surprisingly enough, it is this change, namely the syntactic shift from BH to MH which is the major shift in the history of Hebrew structure. It is not without resemblance with the shift from Latin to Romance, the difference being that Hebrew had lost nominal declension and adopted prepositions already at its early biblical stage while Latin keeps it until quite late. Yet, if the syntactic colouring of BH is to a certain extent akin to that of Latin, MH has an undoubted Romance coloration. This may be due to the very same reasons: like the Romance languages, descended from vulgar Latin, MH was an eminently oral language, in which considerations of communicative efficiency prevailed over literary standards, let alone archaic forms. Early CH, which in this regard followed BH syntax, exhibits at present a trend similar to the one attested in MH as far as determination is concerned, once again as a result of foreign influence -this time not Aramaic but English. Thus, CH has expressions like /z e kujjot adam/ 'human rights', a construct-state where the non-determination of /adam/ 'man' is a calque from English, whilst normative Hebrew syntax commands /z e kujjot ha-adam/ 'The rights of Man'. A similar behaviour is observed for many abstract, mass, collective or otherwise nonreferential or non-specific nouns. A question arising from the rapid evolution of CH is whether it can still be considered a Semitic language from a typological viewpoint. The question in itself is ill posed since 'Semitic', 'Indo-European' and the like are, by definition, genealogical terms, and therefore no specific typological interpretation should be attached to them. Still, since Semitic languages do have a common typological core in the realms of phonology, morphology, syntax and vocabulary, just as do other linguistic families, one can reformulate the question in appropriate typological terms and then try to answer it, provided adequate criteria are carefully selected and defined, and a broad variety of languages from the families under analysis is examined. Failing to do so properly may lead to the mistaken conclusion that CH belongs to a supposed Indo-European type, the Standard Average European (S.A.E.) imagined by Benjamin Lee Whorf. Goldenberg (1996) and [START_REF] Kapeliuk | Is Modern Hebrew the only 'Indo-Europeanized' Semitic Language? And what about Neo-Aramaic?[END_REF] show that CH continues to be a Semitic language not only on a genealogical basis but on typological grounds as well.

Syntax

In terms of word order, BH has the verbal predicate in initial position, with the subject marker affixed to it, then a possible explicit and autonomous nominal or deictic subject in second position and, finally, the other verbal complements. This order 2 is preserved in MH and MdH, whereas in Contemporary Hebrew (CH) the order of the first two components is reversed, under the influence of word order in the European languages spoken by those who reactivated Hebrew at the turn of the 20th century: first comes the nominal or deictic subject, then the verbal or nominal predicate. Only if the clause is subordinate or if it begins with a circumstantial complement does the BH order prevail save when pragmatic reasons decide otherwise, e.g. when the object is focalized, cf. Job 14, 19 / a bani:m ša a qu: mayim/ 'Even stone is eroded by water', litt. 'stones erode waters'. In all cases, the object takes the third position. Nominal sentences begin with the nominal or deictic subject, then comes the nominal or deictic predicate. While CBH is typologically synthetic, the following stages from LBH through MH to CH become more analytic. For instance, it is in LBH (Cant. and Eccl.) that we note the first signs the process whereby /šε-/ (relative) and /l e -/ (dative) merge into /šεl/ (possessive): In oral IH it is employed, by and large, as the main device to express the relation of determination of one noun by another, regardless of the semantic content of this determination -possession, constitution, quality, &c. A non-marked sentence in CBH may be either verbal or nominal. The first type has the finite verb in initial position, with the subject indexed to it either as a suffix (in the perfect aspect) or as a prefix (in the imperfect). An explicit noun or deictic can follow the finite verb, then a verbal direct and/or indirect nominal complement, in this order. If the sentence begins with the complement, the predicate precedes the subject, cf. Gn 1,1 /b e re:si:t bårå  ε lo:hi:m εt hašåmajji:m w e εt håårεc w e håårεc håjtå tohu: wabohu: w e ošek al p e nej t e ho:m/, lit. 'at-first restore-3sg.m.pf God-pl. det.foc./acc. def.-skies conj.-det.foc./acc. def.-earth conj.-def.-Universe be-3sg.f.pf chaos conj.-darkness upon face-gen. abyss'. Direct complements may appear as suffixes on the verb, as may possessors on the noun. Of particular interest in BH syntax is the particle /εt/, to which grammars assign the function of marking the verb's second actant when it is determined. Yet, a thorough analysis proves that it was originally a focalizing particle, which, given the affinities between a determined and animate -hence non-prototypical -object and a subject, prototypically determined and animate, started to be used to distinguish the first from the second. It is /εt/ that fulfills that role because of the inherent affinity obtaining between the pragmatic function of focus and the syntactic one of object. The particle's function shifts then from a merely pragmatic use to a mainly syntactic one, without ever ceasing to play its initially pragmatic role. That is why in BH /εt/ introduces not only direct objects but also subjects (!) of passive verbs and is found even in nominal sentences. In such cases, it clearly plays the role of focalizer [START_REF] Kirtchuk | /et/ ou ne pas /et/: l'actant Y en hébreu et au-delà[END_REF]. The nominal sentence, viz. one in which the predicate is a noun, is prototypically composed of two nouns, the former being the subject and the latter the predicate. A copula is not necessary unless the sentence is marked for tense/aspect. If, though not marked for tense/aspect, a sentence has a third person deictic in agreement with the subject's gender and number, there is no copula but a pragmatic marker of focalization. In other words, thanks to the rich concord system of agreement which ultimately takes in charge the marking of syntactic roles, word order is rather free and may therefore be used for pragmatic purposes, namely for focalization and topicalization. The construct-state is a common semitic morphosyntactic structure which enables a noun to determine a preceding one without a positive autonomous expression other than syntactic juxtaposition and phonological coalescence. Morphophonemic changes may overtly occur on the first noun, the determinatum, if it is a polysyllabic masculine singular, a feminine singular or a masculine plural. In the first case, a syllable is lost or abridged; in the second case its singular feminine suffix /-å#/ assumes its ancient form /at#/; in the thirs case, the suffix /-i:m#/ of the first noun loses its nasal element and /i:/ is separated into two segments, [-ej]. In all cases, the first noun or determinate loses its accent in favour of the determinant. It is the second that bears the definite article /#ha-/ if either the phrase as a whole or its second member is defined. The agreement system is quite developed. The verbal predicate agrees with the subject in gender, number and person, and the attributive noun or deverbative nominal agrees with the kernel-noun in gender, number and determination. The predicative noun or deverbative nominal does not observe agreement in determination with the subject. This corroborates the assumption that the subject function results from the grammaticalization of the topic, while the predicate results from the grammaticalization of the focus, topic and focus being prototypically determined and undetermined respectively. This results from the topic being known information, while the focus is the unknown, new information, that for whose sake the utterance exists in the first place. Arab grammarians understood this who termed the nominal subject /mubtada/ 'initial' and the nominal predicate /habar/ 'information'. BH syntax abounds in parataxis: clauses and sentences are coordinated, mostly by /w e -/, rather than formally subordinated. This does not mean that logical relations do not exist in BH, but that they are expressed otherwise than by conjunctions. Indeed, subordination is expressed mostly by the consecutio temporum, of which, Gn 1,1 quoted above is a fairly good example. The verbal forms and their distribution in the sentence, combined with the scope of uses of the conjunction /w e -/, largely context-dependent, as well as a thorough analysis of the meaning of /br/ (a derivative of b-r; in the pi:el it means 'turn a parcel of bush into an habitable space' and gives also b e riu:t 'health'; the root's meaning in Akkadian is indeed 'clarify, find out' 3 ), show that the proper translation of that verse is 'At first God restored the sky and the earth, because the Universe had been a chaos with darkness upon the abyss's surface'. In BH, there is no copula as such in nominal sentences; if a concording deictic (commonly called 3 rd person pronoun, but see [START_REF] Kirtchuk | LUIT: Language -a Unified and Integrative Theory[END_REF][START_REF] Kirtchuk | LUIT: Language -a Unified and Integrative Theory[END_REF] 4 does occur, it is for in order to focalize the immediately preceding element. CH, on the other hand, again under influence of European tongues, uses the copula as a device to separate the subject from the predicate in nominal sentences, with no pragmatic effect. BH being a rather synthetic language, all finite verbs take a subject affix, but if the object be determined, the bi-or tri-valent verb [START_REF] Tesnière | Eléments de Syntaxe Structurale[END_REF]) can take, in addition, a direct object suffix. Thus, /råi:-ti/ see, past-1sg.subj means 'I saw' and / r e i:-ti:-hå/ see, past-1sg.subj.-3sg.f.obj. means 'I saw her'.

3 I am indebted to my colleague and friend Sh. Izre'el for this remark. 4 What is usually and mistakenly termed '3 rd person' is the entity (be it human or not) not taking part in the speech act as such. The features it partakes with the 1 st and 2 nd are accessory. The only persons in any true linguistic sense and often in any true grammatical sense are those which represent speaker and hearer: the 1 st & 2 nd . [START_REF] Benveniste | Structure des relations de personne dans le verbe[END_REF] intuited this but did not go to the heart of the matter. Evidence is found in each and every realm of linguistic analysis. Morpho-phonologically, the non-person deictics are crosslinguistically either identical to or descended from deictic demonstratives which have nothing whatsoever to do with grammatical person as such, and are clearly different from the radical(s) of both the 1 st and the 2 nd person, which often share one and the same radical, as in Semitic including Hebrew. The non-person can be any noun, nominal or deictic demonstrative, while 1 st and 2 nd person are prototypically only and precisely that: I who speak, and you who listen. The essential difference between on one hand the 1 st & 2 nd persons, on the other hand the non-person is as old as language itself, and like language itself it is still operative. It follows from evolutionary reasons; i.e. from the essentially communicating nature of the former as opposed to the communicated nature of the latter. For a full development, cf. Kirtchuk 2011.

Hebrew conforms to Greenberg's Universals; thus, the attribute (including adjectives, subordinate clauses and genitives) follows the noun and the preposition precedes it. In BH possession is also synthetically expressed, by a mark of the possessor suffixed to the possessum. CH, on the other hand, has no object markers on the verb in the colloquial register but does display them, to some extent, in a literary style or high register, and the possessive markers appended to the noun itself in BH are still appended, but to the particle /šεl/. The exception is a subset of terms denoting body-parts and the extension thereof, namely kinship, which on the grounds of iconicity (see below) readily accept appended possessive marks even in the colloquial registers. Indeed, for those items, suffixation of possessives is the non-marked variant, while the analytical construction denotes an alienable relationship in which the term does not denote a body-part or kinship as such, but is used otherwise -generically, metonymically or metaphorically. Be it as it may, Hebrew never becomes even closely as analytic as French, let alone almost isolating as English. BH makes a clear-cut distinction between definite and indefinite nouns, correlating mostly with presence or absence of the definite article (of deictic origin) /#ha-/ prefixed to the noun. In MH, there is a drastic diminution in the use of this device, the distinction being neutralized in most contexts and expressed, when necessary, by other devices, mostly a deictic demonstrative or a possessive suffix. This attrition of the classical determination device results from Aramaic influence. This stage of Hebrew lost the determination opposition altogether due to the freezing of the definite article /-(h)a#/ suffixed to the noun [START_REF] Greenberg | Universals of Human Language[END_REF]). As we pointed out before, MH syntax differs radically from BH's in many respects. MH verbal system does not have a waw conversivum anymore, since the system is no longer an aspectual one -there is no need, therefore, for a special device in order to attribute a temporal deictic value to verbal forms which encode merely the state of (in)completion of the action. MH verbal system is indeed one in which the erstwhile imperfect aspectual forms have the value of future tense, the erstwhile perfect aspect forms have the value of past tense, and the participial forms integrate the verbal system with the value of present tense. Along with this change there is another major development affecting the MH verbal system, replacing by a syntactic device the aspectual oppositions expressed in CBH by morphological means: it is the emergence of analytic forms consisting of an auxiliary verb /hwj/ 'be' conjugated for person, including gender and number plus the participial form of the (semantically) main verb at the adequate gender and number. Such constructions mark the durative, iterative or habitual aspects, in all tenses and in the imperative mood, e.g. /håjå po:e:l/ 'he used to do'. Under Aramaic influence too the rection of some bi-and tri-valent verbs in MH changes, and the construction with the preposition /l e / replaces the one with εt. In other words, the accusative-direct rection retreats before the dative-indirect one. MH makes extensive use of hypotaxis, and many logically hierarchical relations are expressed by syntactic subordination. The subordinating element in MH is not  a šεr as in CBH but šε as in LBH. Moreover, in MH there is plethora of composite elements including conjunctions such as /keywan šε/ 'as, since', interrogatives such as /ejze/ 'which', /ejmataj/ 'when' (with /ej/ playing a role sensibly equivalent to that of Latin /#qu-/ = English /#wh-/, see note 1 above), prepositions such as /al m e nat še/ 'for', conditionals such as /ilmåle/ 'if not (irrealis)' and lexemes such as /beit midråš/ house of study, pl.

/båtej midrašot/ The morpho-syntactic particularity here, in comparison with BH, is that both elements of the construct-state take the plural suffix.

Iconicity

A brief mention will be made now concerning iconicity, namely the correlation between meaning and form which contradicts to a large extent both Saussure's arbitraire du signe and the generative logic-inspired views on language. Hebrew displays iconicity at all levels and at all stages (Kirtchuk 2000[START_REF] Kirtchuk | LUIT: Language -a Unified and Integrative Theory[END_REF].

To give but a few examples: (a) Classical Hebrew, like Semitic in general, uses gemination, a phonetic mechanism, to achieve morphological and ultimately semantic aims. But not any aim: the gemination of R 2 in the verbal schemata known as 'heavy' conveys a 'gemination', i.e. an intensification, of the action in one of several possible ways: a more determined intention -/šåbar/ 'he broke', /šibber/ 'he broke into pieces'; a greater frequency -/qåpac/ 'he jumped', /qippec/ 'he bounced'; a greater number of actants -/låmad/ 'he learned', /limmed/ 'he taught'; in the nominal domain it is used to convey a consuetudinary or professional activity, cf. /uT/ 'string', /ajjåT/ 'tailor'; /gan/ 'garden', /gannån/ 'gardener'; (b) Iconic, too, is the relationship between roots of the three types R 1 R 2 R 1 R 2 , R 1 R 2 R 2 , and R 1 R 2 R 3 {R 1/2/3 = w/j/n} which exhibit similarity both at the morphological and at the semantic level, cf. /nzl/ 'flow', /zlzl./ 'despise', /zll/ 'eat without consideration for the food', /zwl/ 'cheapen', all of which convey the concept of motion downwards, or /kll/ 'include', /klkl/ 'provide', /nkl/ 'exploit', /klj/ 'consume', /jkl/ 'be able', /kjl/ 'contain', /'kl/ 'acquire and contain by eating / vanquish' (see note n° 9, see also my article on Onomatopoeia in this volume) ; (c) Of the same nature is the fact that causativity, namely the control exerted by one actant upon another, induced by the former to do the action conveyed by the verb, is expressed by morphology, i.e. by a total merger of both action and causation in the framework of a specific verbal scheme; (d) In CH, the oral register does not express possession by suffixes but by constructions with /šεl/, with one exception. Nouns denoting close kinship are often used, including in the colloquial register, with suffixed possessive indices. Thus, the close relationship existing in extra-linguistic reality among kith and kin is reflected in the grammatical closeness expressed by affixation (morphology) rather than by analytic constructs (syntax);

(e) At the syntactic level, adjectives are placed after the noun, but not in an arbitrary order: as in other languages, they obey a gradient of perception, objectivity, concreteness and inherence [START_REF] Posner | Essays on the Nature of Culture, Festschrift for Thomas A[END_REF], cf. The higher an adjective is on that scale, the closer it is to the noun it describes, and if that order be altered on semantic or pragmatic grounds, an intonative pause or an explicit conjuntion is needed, see. (2) above ; moreover only the highest in that scale may substantivize, exactly like in other languages (a blond, a Jew, but not *a tall, *an interesting). Thus, there is a correlation between semantics and syntax, or between meaning and form; (f) As far as lexicon is concerned, concepts of crucial importance (culturally or otherwise) show a wealth of roots expressing categorial shifts, while for less central concepts, a change of category is obtained by grammatical means or is altogether unmarked. No doubt, contemporary evolution -social, technological and otherwise -has an influence on the meaning of many elements. An example of iconicity in the structure of vocabulary: inasmuch as an entity is more central in the language and the culture it carries, it is lexical morphemes that reflect this functional richness. Concepts of crucial importance (culturally or otherwise) show a wealth of roots expressing categorial shifts, while for less central concepts, a change of category is obtained by grammatical means or is altogether unmarked. No doubt, contemporary evolution -social, technological and otherwise -has an influence on the meaning of many elements. Yet, the lexical and semantic basic structure of Hebrew is founded on that of BH, MH and MdHA, and it is iconic, as one can infer from the names of some animals: donkey is /håmo:r, åto:n, ajir/, camel is /gåmål, nåqå, bεkεr/, goat is /tajiš, e:z, gedi:/, sheep is /ajil, kibå, Tålε/ depending on sex and age -the first term referring to the sex or the male adult, the second referring to the female adult and the third to the young one. Other roots exist as well to express additional distinctions -such as a female about to give birth. Such distinctions are linguistically relevant, to this very day, for species that were of great economic and cultural importance at ancient times, and the same distinctions do not exist for unimportant species: goose is /awwåz/, with only morphological changes to express the feminine and diminutive. In other words, the relative value of grammar and lexicon in establishing functional semantic distinctions remains as it was at previous stages of the language. In other words, the relative value of grammar and lexicon in establishing functional semantic distinctions reflects previous stages of the language.

Typological Changes induced by External Influence

Aramaic influence on CBH is restrained to a few borrowings including /j e gar ah a du:tå/ (Gn 31, 47), lit. 'monument of testimony'. It becomes, however, of great importance on LBH and even more so on MH, at all levels: phonological, morphological, syntactic and lexical. Thus, stress accent, oxyton in CBH, becomes paroxyton in LBH and MH; the final nasal /-m#/ becomes /-n#/, and the merger of // with /s/ is completed. These changes affect morphology too since the plural masucline suffix /-i:m#/ becomes /-i:n#/. Some verbal schemata proper to Aramaic emerge in MH such as nitpaal. As for syntax, LBH and definitely so MH lose the so-called 'waw conversivum' which in CBH gives the aspectual forms of perfect and imperfect -påal and yipal respectively -a temporal deictic value, so that /#wa-+ påal/ = future, /#wa-+ jipal/ = past, the participle being a nominal form unmarked for tense. CBH is the only Semitic language to display such a combined aspecto-temporal system. Indeed, the term 'conversivum' hardly suits this waw since it does not convert anything; should we have to choose a more appropriate term, it would be waw temporis or waw ostensivum, since it gives the sign-value (positive or negative, i.e. prospective or retrospective, future or past) of the state's or action's time relatively to that of the utterance. In LBH and MH, much on account of Aramaic and especially Greek influence [START_REF] Rosén | L'He'breu et ses rapports avec le monde classique[END_REF][START_REF] Rosén | Hebrew at the Crossroads of Cultures[END_REF], the system is no longer a twofold aspectual one with a tense-marking device, but a threefold temporal verbal system altogether: the erstwhile perfect påal marks the past tense, the erstwile imperfect jipal the future tense, and the participle po:e:l the present tense. At the same time the verbal construction håjå+ participle emerges to encode for the durative/iterative aspect. Three major syntactic influences of Aramaic on the nominal system are exerted on agreement, determination and genitive constructions: (1) the agreement scheme of nouns may change to match the one of their Aramaic equivalents, e. g. /ådε/ 'field', which entails a feminine agreement under the influence of Aramaic /aqal/ 'id.', (2) the opposition determined -non-determined is no longer expressed by the presence or absence of the definite article /ha-/, which is scarcely used at all, but by means of syntactic devices, and (3) the synthetic construct-state, so prolific in BH, is replaced by a construction with /sàel/ 'of' which can be amplified by a suffixed index on the possessum which agrees with the possessor if the latter is determined. Thus, CBH /ribbo:n håolåm/ is in MH /ribbo:no: šεl o:låm/. At the lexical level, MH borrows from Aramaic many terms and phrases in the legal field, such as /ge:T/ 'divorce', /niksej d e lo nåjdej/ 'real estate' and the like. It is upon Aramaic that Hebrew bestows the part played by Latin in the juridic jargon of the European languages. It is in this respect alone -and by no means at the genealogical level -that one might say that 'Aramaic is Hebrew's Latin'. Following the attrition of final segments marking case in the noun and mode in the verb, classical BH stress fell on the last syllable, but in MH, under Aramaic influence, it shifted to the penultima. IH having been reactivated with a so-called Sephardic pronounciation (which preserves stress and gutturals as in classical BH, but obliterates pharyngalization of the so-called 'emphatic' as well as the distinction between open and close vowels, e.g. /a/ and /å/) stress is like in BH, on the last syllable. Save for loanwords from Yiddish, German and (American) English, Latin words borrowed in their Russian form or Hebrew words bearing a Russian suffix. Yiddish, the Jewish Creole which evolved in the Valley of the Rhine in the 10th-12th centuries on a Germanic grammatical basis and a high ratio of Hebrew and Aramaic lexical elements (later it integrated Slavic elements as well), influenced Hebrew in several ways. The most striking one consists perhaps of the Hebrew words which Yiddish itself had integrated then adapted to its own phonology (which varies according to the dialect), pronouncing them in the peculiar Yiddish manner (which to some extent preserves classical Hebrew characteristics: distinction between /a/ and /å/ and between [t] and [t] (IPA [θ]). Those words, or rather the Yiddish forms of those erstwhile Hebrew words, were reintegrated by IH so as to create doublets both at the semantic and at the phonological levels with the IH normative form. Thus, the oxyton form /ma a sé/ in Hebrew means 'story', whilst the Yiddish paroxyton /májse/ means a long, complicated and often invented tale meant to serve as a pretext for something. Russian has contributed some atone suffixes, of which three are most productive: (1) [čik] which serves both for diminutives -cf. [baxur] 'lad', [baxurčik] 'young lad' -and for nomina agentis, cf. [tikun] 'repair', [tikunčik] 'odd job man'; (2) [-nik] which denotes belonging to a group, a profession, etc., cf. [kibbutznik] 'member of a kibbutz', [garanik] 'owner of a garage', and (3) [-tsia], the Russian equivalent of Latin [-tio(n)], cf.

[inflatsia] 'inflation', [koalitsia] 'coalition', etc. [START_REF] Masson | Langue et Idéologie. Les mots nouveaux en hébreu moderne[END_REF]. From Russian also are certain curses. German and French contributed some terms but play no significant role in terms of grammatical influence. As for American influence, in Israel it is deep and far-reaching, and loan-words from American English are not restricted to the domain of high technology in which they are especially numerous. A syntactic construction inspired on that language, with an ante-posed genitive, is often found in commercial advertising, cf. [dani hovalot], lit. 'Danny Transports' where Hebrew syntax requires [hovalot dani] 'id.'. American isolated words or phrases invade IH conversation mainly among people desirous of showing off their education (which often goes only to a certain point) or their supposed belonging to what they perceive as Western culture. This Weltanschauung characteristic of the Israeli secular middle-class is not necessarily shared by highly educated people, by observant Jews, by the popular class or by the Arab Hebrewspeaking minority.

  1. A new red car = Fr. Une nouvelle voiture rouge = CH [mexonit aduma xadaša] 2. A red new car = Fr. Une voiture rouge neuve (? Une voiture nouvelle rouge) = CH [mexonit xadaša, aduma] or [mexonit xadaša ve-aduma] 3. She's a tall blonde = Fr. C'est une grande blonde = CH [zot blondinit gvoha] 4. ? She's a blonde tall =? C'est une blonde grande = ? [zot gvoha blondinit]

  PF.NOP.SG.M' 2 sar 'tempest' 3 sar 'prince / minister ; PART.PR. 1,2, NOP.SG.M.'

	Tå'am				Taam	Tam
	1 tam 'taste, PF.NOP.SG.M'		2 tam 'goût'	3 tam 'candide'
	Tå'an				Tan
	1 tan 'argument, PF.NOP.SG.M'		3 tan 'chacal'
	jå'ac				'yaac
	1 yac 'counsel, PF.NOP.SG.M'		3 yac 'counsel'
	kå'ab				qaw ; qab
	1 kav 'cause pain, PF.NOP.SG.M'	3 kav 'line'; 'béquille'
	kå'as				'kaas
	1 kas 'be vexed, PF.NOP.SG.M'		3 kas 'wrath'
	må'al			maal	mal
	1 mal 'fraud, PF.NOP.SG.M'	2 mal 'fraud' 3 mal 'cut, circumcise pr. 1,2, NOP.SG.M.'
	må'as				'maa	mas
	1 mas 'disdain, PF.NOP.SG.M'		2 mas 'action'	3 mas 'tax'
	nå'al				naal	nal
	1 nal 'put on a shoe, PF.NOP.SG.M'	nal 'soe'	3 nal 'afore mentioned'
		]			[a]
	/e/ = nå'ar	[e]			'naar	[e]
	/ε/ = 1 nar 'bray, PF.NOP.SG.M' [ε]		2 nar 'young man'	[e]
	CH: tone 1: high på'ar	tone 2: low	tone 3: middle 'paar	par
	1 par 'open, PF.NOP.SG.M'		2 par 'gap'	3 par 'bull'
	bå'al				'baal	bal
	1 bal 'possess a woman, PF.NOP.SG.M SG.M' 2 bal 'husband' 3 bal 'not' (prohibitive) så'ar 'saar sar
	bå'ar 1 bar 'burn, PF.NOP.SG.M SG.M' 1 sar 'storm, 'caar car		'baar 2 bar 'ignorant'	bar 3 bar 'wild'
	2 car ' 'sorrow'		3 car 'narrow'
	gå'al				gal
	1 gal 'deliver, PF.NOP.SG.M' så'al		3 gal 'wave' 'šaal	šal
	1 šal 'question, PF.NOP.SG.M'		2 šal 'step'	3 šal 'take off a shoe '
	gå'ar				gar
	1 gar 'admonest, PF.NOP.SG.M' 'šaar šar
	2 šar 'gate'		3 šar 'sing'

3 gar 'inhabit, pr. 1,2, NOP.SG.M.' då'ak dak 1 dax 'lower, PF.NOP.SG.M' 3 dax 'mortified'

In the terminology popularized by Greenberg it would be VSO. This terminology is inadequate, however, insofar as it (1) mixes a part of speech (Verb) with parts of the sentence (Subject and Object), and (2) implies the existence of the Verb category in language as such, which is wrong on dynamic -synchronic, diachronic, ontogenetic, phylogenetic, creolistic and diaglottic -grounds, and on grammatical as well as pragmatic evidence (Bopp 1807,[START_REF] Kirtchuk | LUIT: Language -a Unified and Integrative Theory[END_REF][START_REF] Parish | What Does It Take To Learn A Verb? A Verb Acquisition Meta-Analysis[END_REF], Barner & Bale 2000),


A Le Quiniou

F Rioual

P Héritier

Experimental study of the bouncing trajectory of a particle along a rotating wall

 K.Allia, Phys.Fluids 6, 1108 (1994)] -in particular, an outcome of this study is that the initial spin of the particle appears to have no effect on the features of the impact as long as the relative velocities at the contact are considered.

Introduction

Impacts of particles on boundaries are still the object of important investigations from material scientists. They represent indeed the basic ingredients to take into account for modelling particulate flows along boundaries. The challenge is to be able to describe these flows in a simple way, using macroscopic mechanical parameters, the energy an momentum exchanges between the colliding objects during the impact. Hence the introduction of a coefficient of restitution in order to describe this energy exchange. Starting from the analysis of Hertz-Mindlin and the analytical theory of Maw [START_REF] Maw | The oblique impact of elastic spheres[END_REF], the Walton model [START_REF] Walton | Granular Solids Flow Project[END_REF] is classically used in order to describe the features of the impact. This is a three parameter model : -two parameters which describe the behaviour of the center of mass : the normal restitution coefficient e n and the friction coefficient µ, -and one parameter which represents the tangential motion at the contact patch produced by the tangential compliance : the tangential restitution coefficient β. Maw [START_REF] Maw | The oblique impact of elastic spheres[END_REF] and Johnson [START_REF] Johnson | Contact mechanics[END_REF] have indeed demonstrated the need to consider tangential elastic compliance over the contact area. This model has received several criticisms, in particular for the determination of the tangential coefficient of restitution. This parameter is supposed to take into account the tangential compliance. For nearly head-on impacts, the tangential compliance induces normally a possible reversal of the tangential component of the relative velocity at contact and this is a typical situation where the value of this tangential coefficient becomes inexact [START_REF] Stronge | Oblique impact with friction and tangential compliance[END_REF]. The effect of the initial spin on the impact has often been omitted in previous experimental studies. This might not be insignificant because collisional flows demonstrate frequently oblique impacts between particles and with boundaries which generate some spin. Recently, a study of the impact of particles with initial spins has been conducted [START_REF] Dong | Experimental study of oblique impacts with initial spin[END_REF]. The authors argued that it remains a challenge to model the event of elastic impacts with initial spins. C.Thornton [START_REF] Thornton | A note on the effect of initial particle spin on the rebound behaviour of oblique particle impacts[END_REF] proposed recently that these aspects of the rebound kinematics can be normalized as soon as we use an effective impact angle, defined as the ratio of the relative tangential to normal surface velocities of the two impacting bodies. The study of the bouncing motion of a particle on a static wall has also been studied in other contexts [START_REF] Falcon | Behavior of one inelastic ball bouncing repeatedly off the ground[END_REF] where the finite number of bounces results from a trade-off between gravity and visco-elastic dissipation at the wall. Recently, the impact of a particle on a rotating plate has been studied experimentally in the case where the particle falls vertically under its own weight. Experiments demonstrated the possibility of rolling without sliding for the particle all along the impact [START_REF] Rioual | impact of a particle along a rotating wall[END_REF].

Here we present a new experimental setup devoted to the study of the trajectory of spinning and bouncing particles along a rotating boundary. The particles considered here are plastic model spheres which are used in air guns (P olyvinylchloride). This setup is inspired partly by machines used for spreading fertilizers in which a quantitative prediction of the flow induced the inertial forces (centrifugal, coriolis) for general granules is not an obvious issue [START_REF] Van Liedekerke | Discrete element simulations of the influence of fertiliser physical properties on the spread pattern from spinning disc spreaders[END_REF]. In the first part of this letter, we present the experimental setup and the experimental procedure used for the study of the trajectories. In the second one, we recall the main features of the model that has been proposed recently for a description of the trajectory. The third part focuses on the experimental caracterisation of the frictional interaction between a particle and the boundary and in particular the determination of the mechanical parameters involved in the model(restitution coefficient e n , friction coefficient µ). In the fourth part, we discuss the features of the trajectory and interpret the experimental results at the light of the model. We show in particular that we are able to predict quantitatively the value of the critical friction coefficient µ for which rolling without sliding appears along the trajectory of the particle.

I. EXPERIMENTAL SETUP

A schematic set-up of the experiment is shown in figure (Fig. 1). The particles considered in these experiments are BB beads of diameter 5.93 ± 0.02, the density is 1.86 ± 0.01(g/cm 3 ) and the mass m is 0.21g. The mechanical properties of the particles have been determined from experiments of binary collisions between these particles [START_REF] Foerster | Measurements of the collision properties of Small Spheres[END_REF] and give : e n = 0.91, µ = 0.19 and E (Pa) = 2.8 •10 9 . In these experiments, the particle is held to a hose by a vacuum created with a vacuum pump (the solenoid valve is opened). In order to release the particle, an electronic device generates a sequence of pulses (not shown in the picture) in order to trigger the camera and to activate the solenoid valve which closes the valve and stops the vacuum. The particle falls without spinning, under gravity, onto the thick rotating plane from a constant minimal height (≈ 5mm.) in order to avoid any height effects [START_REF] Rioual | impact of a particle along a rotating wall[END_REF]. A digital video camera with spot illumination is used to record the trajectory of the particle at a resolution of (1024 * 1024) pixels and a rate of f = 3000 frames per second. A 1mm wide white band is drawn on the equator of spherical particles (with a black background) in order to indicate their orientations and to deduce their angular velocities. Figure 2 shows a typical sequence of the trajectory for a model particle along a rotating plate and Figure 3 shows a typical sequence of its angular velocity (in the fixed frame of the laboratory). These sequences of frames are further analysed using image processing sofware (ImageJ). The measurements of the particle positions and angles give us informations on the radial and rotational velocities and indirectly other quantities like the normal restitution coefficient and the dynamical friction coefficient.

The random errors on the particle position on the rotating plate are estimated as δx = ±2mm (errors on particle and plate positions). The random errors on the model particle angles are δθ = ±5 • . At the end of the plate (ejected radial position x e =25cm), the random errors on the radial velocity are an estimated δVx V x = δx x t+1 -x t = 1% and on the rotational velocity Rδ θ R θ = δθ θ t+1 -θ t = 3%. Statistics based on fifteen samples have been conducted for each configuration (angular velocity of the plate Ω ∈ [500 -1000] rpm, initial radial position x 0 ∈ [1 -8] cm, variation of the plate material). The normality of the population distribution has been tested by a Q -Q plot.

Sondergaard et al 1990 [START_REF] Sondergaard | Measurements of solid spheres bouncing off flat plates[END_REF] showed that the normal restitution coefficient decreases with the ratio of sphere diameter to plate thickness in agreement with the theory of Zener [START_REF] Zener | The intrinsic elasticity of large plates[END_REF]. In this study, we use a plate with a sufficient thickness (5mm.) in order to avoid any reduction of the restitution coefficient related to this effect. Five different surface treatments on the plates have been undertaken in order to modify the characteristics of the interaction and thus to explore the mechanical phase space (coefficient of restitution e n , friction coefficient µ). (I) A stainless steel plate painted black (technical painting Julien noir), (II) A steel plate sand-blasted (sand-blasting), (III) A plate varnished (Vernish astral wood), (IV) A plate polished (with emery paper, P 80), (V) A plate in steel which has been rubber coated.

II. OVERVIEW OF THE BASIC ASSUMPTIONS OF THE THEORY FOR THE PARTICLE'S TRAJECTORY

An analytical treatment of the trajectory of a particle along the rotating vane carried out recently [START_REF] Quiniou | Flow of a particle along a rotating wall[END_REF]. The trajectory of a spherical particle (radius R, mass m and normal contact stiffness K n and dissipation parameter ν) at an initial radial position x 0 in the rotating frame (R ), consists of a succession of bounces followed by a permanent contact of the particle along the plate (see Fig. 4). The theoretical description used is based on the rigid body theory introducing only two mechanical parameters for the impact : a coefficient of restitution e n and a friction coefficient µ. This model is applicable if the dimensionless collision time (N t = Ωt c ) and the centrifugal number (N c = x 0 Ω R/t c ) are small compared to one i.e. the collision is considered as instantaneous and as a collision on a static plate (t c is the collision time on a static plate). This is a valid assumption for most rigid materials. The model predicts in particular the existence of a critical friction coefficient µ between the particle and the plate for which the particle can roll without any sliding in the sticking phase. This critical friction coefficient appears to depend only on the normal restitution coefficient e n of the particle and µ = 1 √ 35 (≈ 0.169) is a good approximation according to the theory at least for high normal restitution coefficients (e n > 0.3). The experimental setup presented here can test precisely these different issues for the trajectory of a spinning particle along a rotating boundary.

III. INTERACTION BETWEEN A MOVING BEAD AND A BOUNDARY

Determining experimentally the mechanical quantities which are relevant for the characterization of the impact in the problem is not a simple task and in particular the value of the friction coefficient (particle/wall).

Firstly, we measured these parameters independantly based on an experiment of collision of a falling bead on a static plate : to determine these three constant parameters, we use the model of Foerster et al 1994 [START_REF] Foerster | Measurements of the collision properties of Small Spheres[END_REF] which is a simplification of the model of Maw et al 1981 [START_REF] Maw | The oblique impact of elastic spheres[END_REF] in the definition of the impact and rebound angles with spherical particles. In this setup, the particle falls from a constant height (h ≈ 25cm) without initial spin under gravity onto an inclined plate from γ = 0 • to 80 • which corresponds to an impact velocity of The velocities before and after impact are decomposed into their normal and tangential components at the impact point (see Fig. 5). The velocity before impact obtained from video analysis is (V x1 , V y1 , θz1 =0) and the final velocity is (V x2 , V y2 , θz2 ). Starting from the rigid body theory, the absence of initial rotational speed gives the expression of the rotational speed for a sphere after impact equal to :

V i = √ 2gh = 2.21 m/s. S t a t i c p l a t e γ V x2 V y2 V i V y1 V x1 θz2 x y θz1 =0 1
R θz2 = 5 2 (V x2 -V x1 ) (1)
The quantity θz2 has been measured directly and also calculated indirectly using equation 1. We find a reasonable agreement between the two sets of data, see figure Fig. 6. The fact that the rotational speed calculated from Eq. 1 is based on the assumption that deformations are small indicates that the rigid body theory is still valid. Gorham and Kharaz [START_REF] Gorham | An experimental study of the elastic rebound of spheres[END_REF] have also drawn the same conclusions about collisions with plastic deformations (aluminium oxide spheres on an aluminium plate).

Following [START_REF] Foerster | Measurements of the collision properties of Small Spheres[END_REF] and varying the inclination of the plate, it is shown that a three parameter model (normal coefficient of restitution e n , tangential coefficient of restitution β, friction coefficient µ) can capture the features of the impact. We define the relative translational velocity at the contact patch before and after impact :

g x1,2 ≡ V x1,2 -R θz1,2 .
Foerster et al propose a nondimensional local angle of contact before and after an impact : Walton's model implies that slipping and sticking regions do not coexist in a given impact. The application of this model leads to a sliding solution of the form :

ψ 1,2 = g x1,2 V y1 (2)
ψ 2 = ψ 1 - 7 2 (1 + e n )µ (3)
For non-sliding collisions (sticking), the obtained solution is :

ψ 2 = -βψ 1 (4)
From the model we can represent the collision diagram i.e. plot the non-dimensional local angle of contact after an impact ψ 2 as a function of the non-dimensional local angle of contact before an impact ψ 1 . From such a plot, the parameters involved in eqs. ( 3) and ( 4) can be used to determine µ and β, respectively.

The experimental plot of ψ 2 as a function of ψ 1 is shown on Fig. 7 for the impact of the plastic particle onto the five different plates. In each case, the two parameters µ and β have been determined.

The values of the impact parameters e n and µ for the five different plates are summarised in the Table I. the dynamic rotating plate) using plate (I). For the dynamical case, we plotted on the same graph the data for the different impacts (from the second to the fourth bounce) varying the rotating velocity of the vane from 500 to 800 rpm. This corresponds typically to a relative impact velocity varying from 1 to 7 m/s. We reproduce again the two distinct regimes observed previously and described in [START_REF] Foerster | Measurements of the collision properties of Small Spheres[END_REF] : (i) a first sticking regime for low values of Ψ 1 and (ii) a second sliding regime represented by a straight line for higher values of Ψ 1 .

For the measurements of impact of model particles on the rotating plate, we observe that the impact angle from the normal is 0 • at the first impact, is 51 ± 2 • at the second impact, is 64 ± 2 • at the third impact and is 71 ± 2 • at the fourth impact for all the experimental conditions (x 0 ∈ [1 -8]cm, Ω ∈ [500 -1000]rpm, variation of plate material Table I). The impact angle is always more oblique than 49 • from the second impact. The spin of the particles has also been determined and following [START_REF] Thornton | A note on the effect of initial particle spin on the rebound behaviour of oblique particle impacts[END_REF] we can define the normalized angular velocity as :

φ i = Rθ • i V ni
where θ • is the spin of the particle and V ni is the relative normal velocity on the wall. The experimental data on the collision diagram have been classified according to this parameter. This classification corresponds in fact to the order of the impacts of the particle along the rotating vane. Linear fits of the data have been done for the different values of φ. For the first impact, the data are scattered and a linear fit is very rough. Indeed, the values of the spin are very small for this impact. For impact 2, we find a good interpolation by a linear curve y = x -1, 1 and for impact 3 by a linear curve y = x -1, 08. In the static case, the fit is y = x -1, 1. For each impact, we note that the impact velocity varies typically from 2 m/s to 7 m/s. According to a previous study [START_REF] Rioual | impact of a particle along a rotating wall[END_REF], the coefficient of restitution e n for the experimental beads varies from the values 0, 9 to 0, 75 in this range of impact velocities. However, we checked that this induces only a discrepancy of 5% on the value of the friction coefficient using equation 3. We find therefore that the difference in the data for different values of φ are not significant.

The rough correspondence between the curves for the two experimental configurations leads us to make the following comments : (i) At first, the collisions in the experiment from the second impact appear to be in the sliding regime whatever the incident angles and the impact velocities on the plates.

(ii) Secondly the experiments show that the initial spin of the particles may be taken into account as long as the formalism of [START_REF] Maw | The oblique impact of elastic spheres[END_REF][START_REF] Foerster | Measurements of the collision properties of Small Spheres[END_REF] is adopted and doesn't have a clear influence on the value of the friction coefficient.

It is also important to note at this stage that a friction coefficient may be determined in a more traditional way following the seminal experiments of Coulomb [START_REF] Coulomb | Théorie des Machines simples[END_REF]. Measurements of the friction coefficient with our model particles have been done by following the motion under gravity of a raft of 9 beads falling along an inclined plate for two different inclination angles (γ = 35 • and 40 • ).

Experimental friction coefficients measured using 5 different treatments on the plate give the following results : µ I = 0.38±0.02 ; µ II = 0.58±0.02 ; µ III = 0.27±0.02 ; µ IV = 0.31 ± 0.02 ; µ V = 0.48 ± 0.02 This leads to a discrepancy ranging from 20 to 50 % between both friction measurements. In order to try to explain this discrepancy, we can notice first that the normal load applied at the contact is much higher in the collision case that in the sliding case (the difference being typically equal to the inertial dynamic load m * dV y dt where V y is the vertical velocity of the bead colliding the surface). If sliding friction is mainly a shearing of adhesiv junctions between microscopical asperities at the contact, then slow sliding friction occurs on a rough contact whereas impact friction may experience more plastic contacts [START_REF] Bowden | The friction and lubrication of solids[END_REF]. [START_REF] Gorham | An experimental study of the elastic rebound of spheres[END_REF] [START_REF] Gorham | An experimental study of the elastic rebound of spheres[END_REF] suggested that the derived value of µ from impact experiments must be interpreted as an effective value which takes into account some plastic deformation, unlike the measurements on inclined plates without deformation. This difference in the values of the friction coefficient might be related to the different modes of sliding between the materials [START_REF] Brach | Impact dynamics with application to solid particle erosion[END_REF].

IV. BOUNCING TRAJECTORY

The measurements of the characteristic quantities for each phase of the trajectory have been done using the experimental setup presented in paragraph I. We consider also typical values x 0 =10cm and Ω = 100 rad/s in order to determine the dimensionless collision time scale N t and the centrifugal number N c ; this gives us the typical values N t = 0.005 and N c = 0.0001.

A. Aerodynamic effects on the trajectory

We checked that the air had no drag effect on the trajectory of our model particles. The typical trajectory of the particle in the rotating frame consists of a first phase of bounces with a decreasing height (cf. figure Fig. 4). We introduce the parametric equations of a bounce numbered (i) without taking into account the air flow i.e. velocities of the particle in the laboratory frame (V xi and V yi ) are supposed to be constant throughout the bounce :

x i (t) = X M cos(ω) -Y M sin(ω) (5) y i (t) = -X M sin(ω) -Y M cos(ω) (6)
We define the position of the plate as a function of the time t : Ω = Ω(t -t i ) + θ i with θ i and t i the condition at the beginning of the bounce : the orientation of the plate with the x -axis and the time. Supposing no air flow effect, the trajectory of the particle as a function of time is linear in the laboratory frame :

X M = x i (t i ) + V xi (t -t i ) Y M = y i (t i ) + V yi (t -t i )
With the digital video camera, we detected the initial conditions at the beginning of the bounce : x i (t i ), y i (t i ), θ i and t i and the positions at each step t throughout the bounce x i (t) and y i (t). Fig. 9 shows the experimental data y i (t) as a function of x i (t). The line is the curve fitting of the Eqs. 5-6 with the experimental data finding the best constraint values : V xi and V yi .

A maximum 3% error rate between experimental and fitted velocities V xi and V yi is observed (x 0 ∈ [1 -8]cm, Ω ∈ [500-1000]rpm, variation of plate material, Table I).

B. Length of the jumping phase

The random errors on the position of the particle are estimated as δy = ±2mm. We consider that the particle is in a sticking phase, if the distance with the plate y i (t) is always smaller than R + δy . Making the hypothesis that tan(Ωt) ≈ Ωt and the main variation of the radial velocity occurs throughout the bounces of the particle (neglecting the variation of the radial velocity during the impacts), we get the limit radial position of the bouncing phase equal to x s = x 0

1-e n according to [START_REF] Quiniou | Flow of a particle along a rotating wall[END_REF]. We give a slightly different equation than in [START_REF] Quiniou | Flow of a particle along a rotating wall[END_REF] as the first impact is not treated separately. For given mechanical parameters Table I, the figure (Fig. 10) represents the experimental and theoretical evolution of the limit radial position of the bouncing phase. A very good agreement is found between the experiments and the theory. The smaller experimental values come from the cut-off in order to determine the end of the successive bounces δ y .

C. Sticking phase

For positions x > x s , the contact between the particle and the rotating plate becomes permanent. We measured the sliding velocity defined as

V s = V x -R θ for each expe- rimental conditions (x 0 ∈ [1-8]cm, Ω ∈ [500-1000]rpm).
The particle is supposed to be in a rolling without sliding regime if the sliding velocity measurement is smaller than the random errors δV s = δV x + δR θ. Figs. 11-12 represent the sliding velocity along the vane with the particle onto the painted and roughen steel plate (x 0 = 1.6cm, Ω ∈ [500 -800]rpm). We observe clearly the appearance of two distinct regimes. The sliding velocity is always greater with plate (I) (µ = 0.175). With the roughen plate (II) (µ = 0.45), the sliding velocity is reaching zero. The particle on plate (I) is supposed to be in a rolling with sliding regime (R + S), whereas the particle on plate (II) is supposed to be in a rolling without sliding regime (R -S). The sliding velocity depends also on the rotation velocity Ω.

In order to estimate the value of the critical friction coefficient µ , Fig. 13 represents the sliding velocity using five different treated materials at a rotating velocity of Ω = 700rpm. (δV s /RΩ = 2.5).

For all plate materials, the sticking phase appears at x = x 0 /(1 -max(e n )) ≈ 13cm. We observe that the sliding velocity decreases with the friction coefficient. The sliding velocity is only greater than the random errors with the painted (plate I) and the varnished (plate III) steel plates. From these data, we can give a frame of the value for the critical friction coefficient : µ I ≤ µ * exp ≤ µ IV with µ I = 0.175±0.005 and µ IV = 0.205±0.003. Varying the velocity of the plate between 500rpm. and 800rpm., we notice that the same estimation of the critical friction coefficient holds in conformity with the theory proposed recently [START_REF] Quiniou | Flow of a particle along a rotating wall[END_REF].

We note also that all the combinations of particle and plate material (Table I) have a fairly high value of normal restitution coefficient : e n ∈ [0.68 -0.88]. Hence the critical friction coefficient estimated experimentally is in very good agreement with the theoretical value predicted for high normal coefficients of restitution (≈ 0.169).

The rotational speed at the limit radial position x s for a particle in a (R + S) regime is :

R θs = R θ1 + 5 2 x 0 Ωµe n 1 + e n 1 -e n (7)
In the same way, with all the particles in a R-S regime, µ = µ = 1/ √ 35 and R θs (µ) is a saturated function of µ. Throughout the first bounce, a small negative rotational speed R θ1 is observed, a feature which is not taken into account in the theory (R θ1 = 5 2 x 0 Ωµ(1 + e n ) > 0 according to the theory). The existence of an initial angular velocity R θ1 can be explained by an effect of the tangential compliance since a small radial velocity V x1 is also observed just after the first impact. The first impact angle occurs always at an impact angle of 0 • from the normal. In these range of values, the tangential compliance is expected to give rise to specific features for the impact such as a negative rebound angle [START_REF] Gorham | An experimental study of the elastic rebound of spheres[END_REF]. Fig. 14 shows the experimental rotational speed at the end of the bouncing phase. The dotted line is the curve fitting of the Eq. 7 with the experimental data finding the best constraint value : R θ1 . A good estimation for the rotational speed is R θs = -0.26x 0 Ω + 5 2 x 0 Ωµe n 1+e n

1-e n .

Conclusion

We presented in this article new results concerning the impact of spinning particles along moving boundaries for different surface properties. We showed experimentally that the bouncing trajectory consists in a succession of rebounds of decreasing height followed by a permanent contact of the particle along the vane. These dynamics can be reproduced by the simple theory proposed recently [START_REF] Quiniou | Flow of a particle along a rotating wall[END_REF] in the limit where the centrifugal number and the non dimensional collision time are small compared to one. The condition for this matching is that the normal restitution coefficient and the friction parameter have to be measured independantly using an experimental device of impact of a falling bead on a static plate according to [START_REF] Foerster | Measurements of the collision properties of Small Spheres[END_REF]. A consequence of this study is that the effect of the initial spin of the particle before each impact can be taken into account by using an apparent impact angle defined by the normal and tangential velocity components of the particle surface as explained recently [START_REF] Thornton | A note on the effect of initial particle spin on the rebound behaviour of oblique particle impacts[END_REF]. This is in fact implicit in the formulation of [START_REF] Foerster | Measurements of the collision properties of Small Spheres[END_REF] for the study of the impact. Also, the tangential restitution coefficient characterizing the tangential compliance doesn't need to be taken into account according to our previous theoretical treatment [START_REF] Quiniou | Flow of a particle along a rotating wall[END_REF] : from the second impact onto the rotating plate, the impact angle is indeed oblique enough to be accurately described by a theory of frictional impact in agreement with [START_REF] Gorham | An experimental study of the elastic rebound of spheres[END_REF]. For values of the friction coefficient higher than a critical value, we observe that the sliding velocity of the particle along the vane cancels and that the particle reaches a rolling without sliding regime (R -S) in agreement with the theory. The model is able to predict quantitatively the critical value of this friction coefficient. Another interesting feature of the experiments is the observed difference in the values of the friction coefficients particle/plate measured from the two different protocols used (impact on a static plate -Coulomb friction experiment) at a low velocity (1 to 2 m/s). In fact, at the scale of the contact, the apparent friction coefficient may involve surfacic properties of the materials as well as volumic properties such that its value may depend on the precise stress path applied at the interface between the two bodies [START_REF] Bowden | The friction and lubrication of solids[END_REF]. This may have some consequences in the determination of the boundary conditions for frictional collisional granular flows because particles may not experience the same friction along the boundary depending on their specific motion (impact or sliding). A deeper analysis of the difference between these two quantities at the scale of the contact will be of much value.

Another possible perpective of this study is to extend the experiments to other kinds of softer particles and surfaces. For the last case, new properties for the impact may be expected as the centrifugal number N c and the nondimensional collision time N t might not be small compared to 1 [START_REF] Quiniou | Flow of a particle along a rotating wall[END_REF]. The influence of the asphericity of the bead has also to be considered. We already observed unexpected bouncing trajectories for angular particles on some surfaces in the present setup.

1 Figure 1 :

 11 Figure 1: Schematic experimental set-up

Figure 2 :

 2 Figure 2: Typical sequence showing the spinning motion of a spherical particle onto the rotating plate.

Figure 3 :

 3 Figure 3: Typical sequence showing the angular velocity of a spherical particle onto the rotating plate.

1 Figure 4 :

 14 Figure 4: Schematic view of the trajectory of a spherical particle along the rotating plate in the rotating frame.

Figure 5 :

 5 Figure 5: Schematic impact of a sphere on an oblique static plate γ. Substripts 1 and 2 refer to initial values and those after rebound, respectively.

Figure 6 :

 6 Figure 6: Rotational speed directly measured and rotational speed calculated from 1 for model particles on surfaces (I) and surfaces (II).

Figure 7 :

 7 Figure 7: Collision diagram : non-dimensional local angle of contact after an impact ψ2 as a function of the nondimensional local angle of contact before an impact ψ1 for collisions of model particles onto five different treated static plates.

2 Impact 1 Figure 8 :

 218 Figure 8: Collision diagram for the static case (fixed plate) and the dynamic case (rotating plate)

Figure 9 :

 9 Figure 9: Experimental trajectory of a plastic particle onto the painted plate (x0 = 1.6cm and Ω = 800rpm). The line is the curve fitting of the Eqs. 5-6 with the experimental data.

Figure 10 :

 10 Figure 10: Experimental and theoretical limit radial positions x s /x 0 as a function of 1/(1 -e n ).

Figure 11 :

 11 Figure 11: Dimensionless sliding velocity along plate (I) (x 0 = 1.6cm).

Figure 12 :

 12 Figure 12: Dimensionless sliding velocity along plate (II) (x 0 = 1.6cm).

Figure 13 :

 13 Figure 13: Dimensionless sliding velocity along the different plate materials (x0 = 1.6cm,Ω = 700rpm)

Figure 14 :

 14 Figure 14: Experimental and theoretical rotational speed at the end of the bouncing phase.

2 Impact 1

 21 /s) Experimental data, static plate (II) Calculated points, static plate (II) Experimental data, static plate (III) Calculated points, static plate (III) on rotating plate (I), Φ i ∈[-0.2 ; 0.03] Impact 2 on rotating plate (I), Φ i ∈[0.6 ; 1] Impact 3 on rotating plate (I), Φ i ∈[1.3 ; 1.7] Static plate (I), Φ i Experimental data, 5 different plates Curve fitting: y=5/2x-0.26

Table I :

 I Summary of the mechanical parameters for the collision of the model particles with the fixed plate.

	Plate material	e n	µ
	plate (I)	0.875 ± 0.02	0.175 ± 0.005
	plate (II)	0.76 ± 0.06	0.45 ± 0.01
	plate (III)	0.68 ± 0.06	0.164 ± 0.005
	plate (IV)	0.88 ± 0.05	0.205 ± 0.003
	plate (V)	0.80 ± 0.06	0.64 ± 0.01

The next figure represents Ψ 2 as a function of Ψ 1 for both experimental configurations (the static plate and

Acknowledgments

We would like to acknowledge a financial support from the région Auvergne (contributing to the PHD grant of A. Le Quiniou). This work also benefitted from the support of the Fédération de Recherche TIMS, CNRS 2856. C.Caroli and T.Baumberger are aknowledged for fruitful discussions concerning the physics of solid friction, M.Y.Louge, C.Thornton, T.Biben, H.H.Shen for their comments about the models of impact and B.Elhedili (an IFMA student) for interesting suggestions about this work.