Laurine Viel

Sandrine Bonnardin

QUESTIONING THE ANALYTICAL FRAMEWORK OF FUNERARY ORNAMENTS IN DIFFICULT ARCHAEOLOGICAL CONTEXTS: THE MEGALITHIC MONUMENTS OF ARLES-FONTVIEILLE (SOUTHERN FRANCE, FINAL NEOLITHIC)

Good morning

Introduction:

Personal ornaments found in funeral contexts have been the subject of research for several decades.

The accumulation and deepening of this research made possible the building of a strong methodological framework. The practice now seems to be quite well established, notably for optimal archaeological contexts with preserved connections, individual graves, and accurate chronologies. It has gradually provided a methodological basis, on which archaeologists have relied to interpret the status of objects and people, funeral practices, etc. However, all these provisions seem to be more questionable in certain cases where the archaeological context is specific and constraining, such as old excavations, or burials without a detailed chronology or connection between the objects and the bones. This can influence interpretations. This is the case for Arles-Fontvieille megalithic monuments. This complex, located in the south-east of France, includes four hypogea and a dolmen, probably built at the end of the 4th millennium B.C. M. Anibert, an historian, mention them in 1779. Most excavations were undertaken in the second half of the 19th century. The quality is variable: emptying for the hypogea of La Source and Bounias, some test excavations for the great hypogeum of Cordes, real archaeological process for the hypogeum of Castelet and the dolmen of Coutignargues.

Since their excavation, these monuments have been the object of constant archaeological research, notably since the late 1990s. Archaeologists highlight the exceptional side of these monuments through two criteria: the original architecture of the hypogea (chambers dug with capstones) and the very large dimensions of the Cordes hypogeum (42,70 meters long and up to 4 meters high). These same researchers sometimes transfer the qualifier of exceptional to the objects contained in these monuments, notably to increase the status of this complex and of its occupants.

But it is a theoretical posture that we must question. Does it reflect reality in what concerns these monuments? these objects? Are all objects exceptional?

USE OF THE TERM "EXCEPTIONAL" BY ARCHAEOLOGISTS: A RAPID INVESTIGATION

To answer these questions, we, archaeologists need to know what we mean by exceptional. We conducted a quick investigation into the use of the term "exceptional" by archaeologists.

If we take the common sense, according to dictionaries, this term designates something that is not included in the general rule: as to its number (synonymous with rare), as to its value, as to its nature.

In particular, what goes out of the usual rule by its high value. If we apply this definition to archaeology, an exceptional object, for example, is thus a rare and/or valuable object. In this investigation, we didn't attempt to distinguish rarity from value, since they may be related, but we identified the criteria used by archaeologists to determine the rarity or unusual value of certain objects, sites and graves.

We took a sample of 55 bibliographical references, in English, French, and Spanish where the term "exceptional" appears. As you can see on the PowerPoint, a lot of various criteria can be considered to characterize the archaeological items as "exceptional": rarity, raw material, quality, important dimensions, long occupation, ... This quick investigation shows that, often:

-the use of the term "exceptional" is subjective. Indeed, there is a various range of criteria.

-But sometimes, the characteristics that are at the origin of the qualifier are not given.

-It is used too often.

-It sometimes provokes circular reasoning.

Is it not significant to note that anthropologists who work on socially valued objects do not use this word to describe an object category? They prefer to use: "precious objects", "sacred objects", "signs", "objects of power", ... On the other hand, there is also a lack of accuracy in the vocabulary for objects that seem more common, banal. This type of material is rarely used to question status. In the studies of Fontvieille monuments, archaeologists do not use these objects to address the question. Only so-called exceptional objects are considered.

So, as archaeologists, we have practice problems with these corpuses. It is necessary to step back and ask ourselves on the way we question the status of objects. Back then, there had to be nuances in the categories of status, between the most socially valued objects and their opposites. We must reintroduce these shades to consider all the objects.

DIFFERENT CATEGORIES OF STATUS? THE EXAMPLE OF ARLES-FONTVIEILLE ORNAMENTS.

We selected three types of objects from Arles-Fontvieille megalithic monuments that I'm going to present according to the importance that seems to be attributed to them. For each example, I'm going to present different intrinsic characteristics divided in two categories: those for which it seems obvious to assign a status and those that could question this status.

An undeniably high added value object: the golden bead of the hypogeum of Castelet

There is a good chance that the first example -the golden bead of Castelet-had a strong social value in the eyes of Neolithic populations. Indeed, the raw material of this bead is rare, and the populations probably acquired it by exchange. If there are larger objects of the same type, however, the one of Castelet has an unequalled weight in the Neolithic (36.84 grams). In addition, it appears to have been the subject of significant technical investment, particularly in the final polishing. Thanks to its weight, its material, and its low frequency (less than twenty in Europe), the golden bead of the Castelet hypogeum seems to stand out from the rest. However, unlike other Arles-Fontvieille elements, it was probably used.

The turquoise beads of the hypogeum of Castelet and the dolmen of Coutignargues

The second example, the turquoise beads are generally considered as socially valued object because of their rare raw material, but less than the golden bead. In addition, other characteristics seem to classify these beads in the socially valued objects:

-the material deposits are far from Arles-Fontvieille, -their important number within Arles-Fontvieille (80), -and the fact that this type of object is infrequent.

In southeastern France, only six Neolithic sites delivered turquoise beads, and their number did not exceed 5. We can also add that these beads are little or not used. It is however necessary to note the heterogeneity of the shapes and dimensions, as well as the absence of finishing of the turquoise objects. Indeed, unlike other beads, these have not been polished. We can always observe the shaping marks. These criteria could nuance their social value.

The discoid beads in steatite of the hypogeum of Castelet and the dolmen of Coutignargues

For the third example, we decided to show you objects that seem more common. Indeed, the discoid steatite beads are frequently found in the sites of the final Neolithic and this raw material is often used for the manufacture of ornamental elements. Indeed, according to some studies, 53% of the studied sites have elements in steatite. In another example, on 83 sites where discoid beads have been found, H. Barge identified 56 of them with steatite beads. However, these objects are present in large numbers in Fontvieille. They also have calibrated dimensions, characteristics generally used as an indication of a higher status.

The three examples presented show that all objects have to be studied, even those whose status seems most obvious. Indeed, by considering various criteria, we saw that the golden bead whose material is rare, is used, whereas the turquoise beads, whose material is slightly more frequent, are not. Do these ornamental elements, both seen as strong social markers, have the same status? All too often, objects are classified between those that are socially valued and those that are not, but the preceding examples show that it is necessary to reintroduce nuances between them.

To do this, we must consider a certain number of intrinsic characteristics of the object such as: We also have to integrate the results of the technological study, such as the state of progress in the chaîne opératoire, the uniformity of production, in other words whether or not there is standardization of objects, the investment in production, and the know-how.


It is also necessary to consider the results of functional studies: have the ornaments been worn or not? and in which way?

It seems important to take into account as many intrinsic characteristics as possible when we got into the question of the object status. However, we must think of the meaning and interpretation of these criteria. Indeed, a characteristic can be interpreted as a sign of a socially high value or the opposite. If we take the example of the use of objects, a new object and a very worn object can be interpreted as socially valued elements. In other Neolithic contexts, the hyper-standardization of dimensions is seen as indication of socially valued objects. Of course, the interpretation of the intrinsic characteristics must be made according to the context, but for the ornaments of the Arles-Fontvieille monuments, these parameters were not all the time taken into account.

Conclusion

Archeological reasonings are based on comparisons. There is no comparison for Arles-Fontvieille monuments. That's why the interpretations are less rigorous. So, we have, as archaeologists, a real choice of scientific strategy. How do we prioritize data? What is important to classify an object in one status or another? Its use or the rarity of its raw material? Its hyper-calibration or the distance of the deposits? Without even mentioning the abusive and subjective use of the term "exceptional", the vagueness in its definition, the minorization of more banal objects that conceal part of reality, we must face a real scientific problem. To address questions of object status, it is therefore highly necessary to construct a rigorous interpretative framework based on well-defined criteria and taking all objects into account. The natural temptation of the scientist would be to prioritize criteria to develop categories, but should we do so? can we do without them? We see here, the difficulty of the archaeologist's practice.

To illustrate our remarks, I will end with this quotation from P. Lemonnier, demonstrating that important objects are not necessarily beautiful or remarkable.

« Les archéologues noteront que certains de ces objets formidablement importants pour un groupe et pour les relations entre individus qui le constituent sont malheureusement impossible à repérer : un « fabuleux » objet sacré des Anga ressemble à s'y méprendre à n'importe quel paquet magique utilisé par ces groupes [Lemonnier, 2006] ; un tambour ankave est parfaitement banal, et n'a rien à voir, en particulier, avec les « splendides » objets de la Côte sud de la Nouvelle-Guinée montrés dans les vitrines du musée du quai Branly. » Lemonnier 2012 p. 287

  The raw material o Physical properties: color, gloss, etc. o The rarity of deposits and raw materials o The distance of the deposits, which require to integrate a network of exchange to be supplied  The morphology of the object o Shape o Dimensions  The frequency in the sites  The number of objects of the same typology and material in the site or grave.


A Alkurdi

C Adessi

S Li

K Termentzidis

S Merabia

Thermal transport across nanometre gaps: phonon transmission vs air conduction

Keywords: numbers: Thermal conduction in metals and alloys and semiconductors, 66.70.Df, -Lattice dynamics crystals (see 63), Phonons scattering by, 72.10.Di

Heat transfer between two surfaces separated by a nanometre gap is important for a number of applications ranging from spaced head disk systems, scanning thermal microscopy and thermal transport in aerogels. At these separation distances, near field radiative heat transfer competes with heat transfer mediated by phonons. Here we quantity the contribution of phonon assisted heat transfer using lattice dynamics combined with ab-initio calculations. We clearly demonstrate that phonons dominate by far heat transfer for subnanometre gaps. Strikingly, we conclude that even in the situation where the gap is filled by air molecules, phonons provide the dominant energy channel between the two solids nearly in contact. Our results predict orders of magnitude enhanced phonon heat transfer compared to previous work and bring forward a methodology to analyse phonon transmission across nanoscale vacuum gaps between apolar materials.

Heat may be transferred by three main mechanisms namely conduction, radiation and convection [START_REF] Incropera | Fundamentals of Heat and Mass Transfer[END_REF]. Convection occurs when heat is transported by the macroscopic motion of a supporting medium. Heat conduction is also mediated by a supporting medium, and usually not relevant in vacuum : it is of common sense that two bodies in vacuum exchange heat only through radiation. The situation becomes less clear however at the nanoscale, when the separation distance between two bodies is in the nanometre range. At these length scales phonons may be transmitted across the gap between the two solids and compete with radiative heat transfer thus contributing in the heat exchange between the two bodies.

Recent experimental investigations have reported measurements of heat transfer in the extreme near field regime, where the separation distance between two objects is in the nanometer range [START_REF] Cui | Study of radiative heat transfer in Angstrm-and nanometre sized gaps[END_REF][START_REF] Kloppstech | Giant heat transfer in the crossover regime between conduction and radiation[END_REF]. While one study shows moderate deviations to near field predictions (Rytov's theory) [START_REF] Rytov | Principles of Statistical Radiophysics[END_REF], the other has reported orders of magnitude enhancement. In this Letter, we quantify the phonon contribution to heat transfer in the ultra near field regime on the basis of ab-initio based lattice dynamics calculations. This method enables us to accurately account for phonon dispersion in the two materials nearly in contact. We demonstrate that at the nanometre scale, phonons are the main energy carriers flowing across the gap, wether it is filled or not with air molecules.

Heat transfer between two bodies separated by small distances has attracted the attention of physicists for decades [START_REF] Cahill | Nanoscale thermal transport II[END_REF][START_REF] Cravalho | Effect of small spacings on radiative heat transfer between two dielectrics[END_REF][START_REF] Hargreaves | Anomalous radiative transfer between closely-spaced bodies[END_REF][START_REF] Domoto | Experimental investigation of radiative heat transfer between metallic surfaces at cryogenic temperatures[END_REF]. Early studies were motivated by the possibility to observe deviations to Planck's theory of radiation. These pioneering measurements were performed at low temperatures, when Wien's thermal wavelength is macroscopic hence facilitating the observation of deviations at relative large separation distances [START_REF] Kralik | Strong near-field enhancement of radiative heat transfer between metallic surfaces[END_REF]. The last decade witnessed intensive effort toward the evidence of extraordinary heat flux in the near field regime [START_REF] Kittel | Near-Field heat transfer in a scanning thermal microscope[END_REF][START_REF] Rousseau | Radiative heat transfer at the nanoscale[END_REF][START_REF] Shen | Surface phonon polaritons mediated energy transfer between nanoscale gaps[END_REF][START_REF] Narayanaswamy | Thermal near-field radiative transfer between two spheres[END_REF][START_REF] Altfeder | Vacuum phonon tunneling[END_REF][START_REF] Ottens | Near-field radiative heat transfer between macroscopic planar surfaces[END_REF][START_REF] Lim | Near-field thermal radiation between doped silicon plates at nanoscale gaps[END_REF][START_REF] Kim | Radiative heat transfer in the extreme near field[END_REF][START_REF] Song | Radiative heat conductances between dielectric and metallic parallel plates with nanoscale gaps[END_REF][START_REF] St-Gelais | Near-field radiative heat transfer between parallel structures in the deep subwavelength regime[END_REF], ever pushing the limits of separation distances.

These fundamental investigations have been fostered by the technological side of the problem. Radiative heat transfer across microscale gaps is at the core of near field thermophotovoltaics, an emerging field of investigation [START_REF] Fiorino | Nanogap near-field thermophotovoltaics[END_REF]. At shorter separation distances, the applications concern thermal rectifiers [START_REF] Otey | Thermal rectification through vacuum[END_REF], heat assisted magnetic recording [START_REF] Wu | Nanoscale heat transfer in the head-disk interface for heat assisted magnetic recording[END_REF] and scanning thermal microscope [START_REF] Gomés | Scanning thermal microscopy: a review[END_REF]. Thermal transport across nanocavities controls also the thermal conductivity of silica aerogels [START_REF] Zeng | Pore size distribution and apparent gas thermal conductivity of silica aerogel[END_REF].

Despite its technological importance, thermal transport between two bodies nearly in contact still resists a full theoretical treatment. One of the yet unsolved question is how to describe the gradual transition between radiative and conductive heat transfer in the extreme near field regime. Depending on the separation distance, different regimes may be distinguished. Indeed, when two bodies are separated by macroscopic distances, thermal transport is very well described by Planck's blackbody radiation law [START_REF] Incropera | Fundamentals of Heat and Mass Transfer[END_REF][START_REF] Planck | The theory of Heat Radiation[END_REF]. When the separation distance becomes comparable to Wien's thermal wavelength (λ 10µm at 300 K), radiation can exceed by orders of magnitude blackbody law. In this regime, photons emitted by one of the two media tunnel across the gap, and the overlapping evanescent waves yield enhanced heat transfer. At the other extreme when two bodies are in contact, heat transfer is mediated by phonon transmis-sion. At nanometre distances, the distinction between radiation and conduction becomes somewhat blurred, and this is precisely this regime that we investigate in this Letter.

Several mechanisms have been invoked to come into play when the separation distance is ultra small [START_REF] Chiloyan | Transition from near-field thermal radiation to phonon heat conduction at sub-nanometre gaps[END_REF][START_REF] Prunnila | Acoustic phonon tunneling and heat transport due to evanescent electric fields[END_REF][START_REF] Ezzahri | Vaccum-induced phonon transfer between two solid dielectric materials: illustrating the case of Casimir force coupling[END_REF][START_REF] Xiong | Classical to quantum transition of heat transfer between two silica clusters[END_REF]. They have in common to involve the coupling between phonons and electric fields, a situation relevant to piezoelectric or polar materials. Here, we consider phonon contribution to heat transfer across apolar materials. Our calculations show that phonons are the main energy channel for nanometre gaps, thus correcting by orders of magnitude previous estimates of phonon assisted thermal transport [START_REF] Pendry | Phononassisted heat transfer between vacuum-separated surfaces[END_REF].

To calculate the contribution due to phonon across nanoscale gaps, we employ ab-initio based lattice dynamics (aiLD) [31,[START_REF] Alkurdi | results from ab initio lattice dynamics calculations[END_REF]. The principle of the method is inspired by Zhao and Freund work [33], which considered empirical potentials to describe the atomic lattice dynamics at the interface. We basically extend Zhao and Freund's method obtained from ab-initio first principles calculations. In brief, the system is divided in three regions namely, the left and the right leads and the interface, as illustrated in fig. 1. In the bulk leads, we solve the dynamical equations:

(φ α,β -mω 2 δ α,β )u β (ω) = 0 (1)
where Φ α,β denotes the harmonic force constant tensor, ω is the phonon frequency and u β (ω) denotes the components of the atomic displacement along the direction β.

In the junction region, the equations to be solved write :

(φ AA α,β -m A ω 2 δ α,β )u A β (ω) + φ AB α,β u B β (ω) = 0 (2) φ BA α,β u A β (ω) + (φ BB α,β -m B ω 2 δ α,β )u B β (ω) = 0 (3)
here the subscripts A, B denote the two materials, and we have introduced the corresponding Hessian matrices φ AA , φ BB , φ AB , φ BA with obvious notations. The displacement u A in the incoming medium may be split in an incoming wave having a wavevector k i and n r reflected waves, each having a wavevector k r . Similarly, the displacement u B in the other medium is a sum of n t waves characterized by their wavevectors k t . The numbers n t , n r and the expressions of the wavevectors k r , k t are given by the conservation equations at the interface, see [START_REF] Alkurdi | results from ab initio lattice dynamics calculations[END_REF]33] for further details. From the knowledge of the transmitted displacement, one can infer the mode dependent transmission coefficient and interface conductance :

T (k t , ν) = ρ A ρ B v z g,t .|A t | 2 v z g,i .|A i | 2 (4)
where ν is an index denoting the branch index, ρ A and ρ B are the mass density characterizing the two materials respectively, v z g,t is the group velocities of the transmitted phonons projected along the direction perpendicular to the interface, A t and A i are the amplitudes of the transmitted and incident wave respectively. The modedependent thermal conductance has the expression :

G(k t , ν) = 1 V v z g,t ω ∂f (ω, T ) ∂T T (k t , ν) ( 5
)
where V is the volume of the system and f denotes the phonon occupation density.

For gold, the bulk harmonic force constants are calculated with the code VASP [START_REF] Kresse | Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[END_REF][START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF] using the Generalized Gradient Approximation (GGA-PBE) [START_REF] Perdew | Generalized gradient approximation made simple[END_REF][START_REF] Perdew | Erratum: Generalized gradient approximation made simple[END_REF] . For silicon, we extracted the values from the literature [START_REF] Aouissi | Phonon spectra of diamond, Si, Ge, and α-Sn: Calculations with real-space interatomic force constants[END_REF]. In the S1 of the Supplementary material [39], we illustrate the good agreement between the calculated bulk phonon spectra and available experimental data.

For the interaction between the materials across the gap, we consider a Lennard-Jones potential [START_REF] Israelachvili | Intermolecular and Surface forces[END_REF]:

Φ zz (z) = 8πρ σ σ z 11 - σ z 5 ( 6
)
where ρ is the material density and z is the distance to the other medium. The Lennard-Jones parameters , σ are extracted from [START_REF] Heinz | The Journal of Physical Chemistry C, Accurate simulation of surfaces and interfaces of face-centered cubic metals using 12-6 and 9-6 lennard-jones potentials[END_REF] for metals, and for semiconductors we used the values derived from the knowledge of the material Hamaker's constant [START_REF] Israelachvili | Intermolecular and Surface forces[END_REF], as listed in S2 of is the total interaction potential per unit of surface between the two solids. Further details may be found in the S3 [39]. Last, the contribution due to the presence of air molecules in the gap is estimated following [START_REF] Devienne | [END_REF], as detailed in S4 of [39].

Figure 2 presents the atomistic aiLD calculations results for the thermal transport across the gap between two gold solids. The calculated conductance due to phonons is compared to the contribution due to different energy channels. Clearly, the contribution due to phonons is by far the largest, for the range of gap widths analyzed here. It is orders of magnitude higher than black body conductance G BB 6 W/m 2 /K [START_REF] Incropera | Fundamentals of Heat and Mass Transfer[END_REF]. Less expectedly, phonon heat transfer beats near field radiative heat transfer also by orders of magnitude. Last, the contribution due to phonons is higher than air conduction for gap widths smaller than 1 nm. This implies that if the gap is filled with air molecules, long range interactions between the two solids contribute much more to the heat transfer than ballistic transport mediated by the molecules. It is remarkable that the ab-initio calculations yield conductance levels comparable to the AMM predictions. We will rationalize this observation through the analysis of the spectral phonon transmission across the gap. Note that the dip present in the AMM conductance for small gaps is related to the non monotonicity of the Lennard-Jones spring constant, driven by short-range repulsive interactions.

Figure 2 demonstrates that the same qualitative conclusions may be drawn for the silicon/gap/silicon system. In this latter case however, the atomistic calculations give conductance levels lower than the AMM predictions. Nevertheless, phonon contribution still dominates air conduction below 1 nm.

The dominance of phonon over air conduction was shown here at room temperature. To appraise the generality of this behavior, the temperature dependence of the conductance characterizing the two main energy channels-phonon transmission and air conductionhas been reported in fig. 3. Clearly over the wide range of temperatures considered, the contribution due to phonons is the highest. Only at cryogenic temperatures, a very limited number of acoustic modes is populated, and air conduction may become the leading channel.

To get insight in the microscopic mechanisms behind thermal conduction in the gap, we discuss now the spectral contribution to the interfacial heat transfer mediated by phonons. Of particular interest we analyze how acoustic models can accurately capture the contribution of heat flow due to phonons. We concentrate first on the case of gold, for which the spectral transmission and conductance are plotted in fig. 4. For all the gap widths analyzed, only low frequency phonons are transmitted across the gap. This behavior is well captured by AMM models at low frequency, while these latter models tend to overestimate slightly phonon transmission for higher frequencies. On the opposite, the AMM predictions underestimate somewhat the conductance, except for the narrowest gap analysed. This conclusion is in full line with the total conductance calculated and presented in fig. 2. The relatively low values of the conductance pre-dicted by AMM may be explained by the underestimation of the density of intermediate frequencies, contributing to undervalue the spectral conductance.

We now turn to the case of silicon, as illustrated in fig. 5. Here a different scenario emerges : the transmission coefficient of long wavelength phonons is low, and only intermediate frequencies phonons can tunnel across the gap. But even the transmission coefficient of these modes is overestimated by AMM, leading to a discrepancy in the spectral conductance. This analysis explains the relatively low conductance of silicon interfaces, as displayed in fig. 2. [START_REF] Chapuis | Effects of spatial dispersion in near-field radiative heat transfer between two parallel metallic surfaces[END_REF]. Bottom : Thermal boundary conductance between two silicon solids separated by a nanometric gap of width d. Continuous red line is the generalized AMM model. Near-field radiative prediction is taken from [START_REF] Sellan | Phonon transport across a vacuum gap[END_REF]. Our calculations involve so far phonon transmission, and it is legitimate to wonder wether alternative energy channels may contribute to heat transfer across the gap. As shown experimentally in [START_REF] Kloppstech | Giant heat transfer in the crossover regime between conduction and radiation[END_REF], electron tunneling may occur only when the gap distance becomes smaller than 0.2 nm, thus precluding any direct electronelectron scattering mechanism for larger separation distances. However, metal electrons may play an indirect role in heat transfer through their couplings with phonons. Indeed, electrons couple with phonons in different ways, as summarized in [START_REF] Lombard | Influence of the electron-phonon interfacial conductance on the thermal transport at metal/dielectric interfaces[END_REF]. Of particular interest here, is the situation of weak electron-electron coupling through the gap. Under these conditions, the electronic temperature should obey an adiabatic condition at the boundaries. In the Section S5 of [39], we show that the effect of the electron-phonon coupling is to reduce the effective thermal boundary conductance by an amount :

0 0,3 0,6 0, 9 1,2 1,5 d (nm
G eff G/(1 + 2G/ k p G ep )
, where G is the phonon-phonon conductance that we already calculated, k p is the phononic contribution to the metal conductivity and G ep is the electron-phonon coupling. This latter expression generalizes the expression derived in [START_REF] Reddy | Role of electronphonon coupling in thermal conductance of metalnonmetal interfaces[END_REF] in the case of metal/semiconductor interface. Considering the values of k p and G ep for gold [START_REF] Jain | Thermal transport by phonons and electrons in aluminum, silver, and gold from first principles[END_REF]48] k p = 2 W/mK; G ep = 2.5 10 16 W.m -3 .K -1 [START_REF] Jain | Thermal transport by phonons and electrons in aluminum, silver, and gold from first principles[END_REF]48]. The resulting values of the conductance is 0.11 MW.m -2 .K -1 , which is higher than the conductance due to the ballistic motion of air molecules. Note that gold has a relatively low electron-phonon coupling constant, so that the electronphonon interfacial conductance is even higher for other metals (0.62 MW.m -1 .K -1 for aluminium). Interfacial electron-phonon transfer will therefore not impede interstitial heat transfer below air conduction level.

In summary, we investigated phonon mediated thermal transport in the extreme near field regime using ab-initio lattice dynamics calculations. We demonstrated that for nanometre gaps, phonons are the main energy carriers exceeding by orders of magnitude near field radiative heat transfer. Strikingly, the contribution of phonons exceeds also largely ballistic transport assisted by gas molecules in the gap. This implies that even in the situation where the gap is filled with air, long range van der Waals interactions provide the dominant heat transfer mechanism. These results open the door to quantify systematically heat transfer mediated by phonons between apolar materials.

FIG. 1 .

 1 FIG. 1. (Color online) Illustration of the configuration considered : two semi-infinite solids separated by a gap of width d.

  [39]. The atomistic calculations will be compared with the predictions of a generalized acoustic mismatch model (AMM), describing phonon transport across the solid/vacuum gap/solid interface. In this model, the transmission coefficient is supposed to be given by T (ω) = 1/(1 + (ω/2K) 2 z 2 m ) where z m = ρ m c is the acoustic impedance of the material with ρ m and c the mass density and speed of sound respectively, andK = n s ( d 2 Vdz 2 ) z=h is the interface compliance, with n S the density of surface atoms and V (z) = 8πρ 2 σ

FIG. 2 .

 2 FIG. 2. (Color online)Top : Thermal boundary conductance between two gold solids separated by a nanometre gap of width d, calculated at room temperature. Near-field radiative predictions are taken from[START_REF] Chapuis | Effects of spatial dispersion in near-field radiative heat transfer between two parallel metallic surfaces[END_REF]. Bottom : Thermal boundary conductance between two silicon solids separated by a nanometric gap of width d. Continuous red line is the generalized AMM model. Near-field radiative prediction is taken from[START_REF] Sellan | Phonon transport across a vacuum gap[END_REF].

FIG. 3 .

 3 FIG. 3. (Color online) Thermal boundary conductance between two gold solids (top) and two silicon solids (bottom) separated by a nanometre gap d as a function of temperature. The contribution due to air conduction is shown with dashed purple lines.

FIG. 4 .

 4 FIG. 4. (Color online) Phonon transmission coefficient and spectral conductance between two gold solids separated by a nanometre gap d, as a function of frequency. The solid lines display the atomistic calculations while the dashed lines are the AMM predictions.

FIG. 5 .

 5 FIG. 5. (Color online) Same as fig. 4 for Silicon.

The authors acknowledge fruitful discussions with P.-O. Chapuis, T. Albaret, A. Ayari and P. Vincent. Financial support from Labex projet iMust ATTSEM and H2020 programme FET-open project EFINED (number 756853) is acknowledged.


Martin Cooke
email: m.cooke@ikerbasque.org

María Luisa

García Lecumberri
email: garcia.lecumberri@ehu.es

Jon Barker
email: j.p.barker@sheffield.ac.uk

Ricard Marxer
email: ricard.marxer@lis-lab.fr

Lexical frequency effects in English and Spanish word misperceptions

come

Introduction

It is a common experience for listeners to misperceive words under challenging conditions, but the manner in which degraded sensory evidence and prior language experience interact to produce the resulting 'slips of the ear' is poorly understood. One form of prior information that listeners might be forced to use in noise is lexical frequency. It has long been known that common words are more likely to be correctly recognised in noise than less frequent words [START_REF] Howes | On the relation between the intelligibility and frequency of occurrence of English words[END_REF][START_REF] Savin | Word-frequency effect and errors in the perception of speech[END_REF] but there are conflicting findings as to whether misperceptions are themselves more common words than corresponding intended 'target' words in noise.

Several studies have examined lexical frequency effects in naturalistic compilations of reported real-life misperceptions [START_REF] Browman | Errors in Linguistic Performance: Slips of the Tongue, Ear, Pen and Hand[END_REF][START_REF] Bond | Morphological errors in casual conversation[END_REF][START_REF] Tang | Measuring segmental and lexical trends in a corpus of naturalistic speech[END_REF] . Using a meta-corpus composed of previous compilations of misperceptions, Tang [START_REF] Tang | Naturalistic speech misperceptions[END_REF] found an inconsistent pattern of lexical frequency effects across corpora, but overall, misperceptions were not more common words than target words. One issue with naturalistic corpora is the paucity or absence of metadata describing the context in which each misperception occurred. For example, neither audio evidence for each speech token nor information about the presence, nature and level of any maskers is available for further analysis.

Very few studies have measured lexical frequency effects in controlled masking conditions. Pollack et al. [START_REF] Pollack | Analysis of incorrect responses to an unknown message set[END_REF] analysed incorrect responses from an earlier study 8 in which listeners identified 144 distinct monosyllabic English words belonging to one of eight frequency classes, presented in white noise at signal-to-noise ratios (SNRs) in the range -5 to +25 dB. Pollack et al. found the median lexical frequency of incorrect responses to be independent of the word frequency class of the stimulus. However, listeners reported higher frequency misperceptions at lower SNRs. Listeners in a study by Felty et al. [START_REF] Felty | Misperceptions of spoken words: Data from a random sample of American English words[END_REF] identified subsets of a 1428 English word sample presented in 6-talker babble at SNRs of 0, +5 and +10 dB. A clear lexical frequency difference effect was observed: misperceptions were more common words than target words. A similar study 10 using Spanish words presented in five maskers at SNRs in the range -13 to +1 dB found that, across maskers, the lexical frequency of misperceived words was significantly higher than target words. However, no breakdown by masker type was presented.

Taken together, previous studies present an inconsistent picture of whether misperceptions reported by listeners under conditions of actual or potential masking (the latter corresponding to the case of naturalistic corpora) tend to be more common than target words. This is not altogether unexpected, since the varied masking conditions employed in the these studies might have modulated the role of lexical frequency in different ways. One key distinction is between energetic and informational masking. While pure energetic maskers such as stationary or modulated noise act to distort or partially remove acoustic evidence for the target word, speech-based informational maskers can in principle contribute fragments of their own acoustic-phonetic information to the melange which forms the basis for a listener's lexical decision, enabling misperceptions to result from misallocation of masker fragments to the final word interpretation. The current study of lexical frequency effects in noise was motivated by the absence of prior studies involving comparisons of (i) more than one masker; and (ii) maskers with both an energetic and informational component.

Datasets

Lexical frequency effects were investigated for consistent word misperceptions in noise in two recent, extensive, open-source datasets of Spanish (SP) [START_REF] Tóth | A corpus of noise-induced word misperceptions for Spanish[END_REF] and English (EN) words [START_REF] Marxer | A corpus of noise-induced word misperceptions for English[END_REF] .

Consistent misperceptions are defined in these datasets as tokens for which no fewer than six listeners reported the same misperception in response to a given target word presented in noise. Both datasets were elicited in a similar manner, but while the EN dataset used three maskers (speech-shaped noise, SSN; 3-talker babble-modulated noise, BMN3; 4-talker babble, BAB4), the SP dataset additionally employed 1-talker babble-modulated noise (BMN1) and 8-talker babble (BAB8). Babble maskers were generated by random concatenation of target words to reach the required babble density [START_REF] Tóth | A corpus of noise-induced word misperceptions for Spanish[END_REF][START_REF] Marxer | A corpus of noise-induced word misperceptions for English[END_REF] . Misperceptions were elicited at a range of SNRs (Table 1), values chosen in pilot tests to maximise the chance of consistent confusions, motivated by the finding that too-high SNRs lead to few errors, while too-low SNRs tend to produce inconsistent errors.

The online Spanish and English corpora contain 3235 and 3207 misperceptions respectively. For the current study these counts were reduced to 3126 and 3198 after excluding tokens based on the following criteria: (i) 82 Spanish confusions were found to result from SNRs outside the desired SNR range 11 ; (ii) for 11 examples (8 Spanish) no lexical frequency data was available for the confused word; and (iii) for 25 examples (19 Spanish) the reported misperception was not present in the relevant pronunciation dictionary. Table 1 provides a breakdown of the number of misperceptions for each language/masker pairing along with details of the SNRs that led to the misperceptions. One difference between the two published corpora lies in the source of lexical frequency estimates for target and misperceived words. Estimates for the SP dataset are derived from the CREA Spanish word frequency list [START_REF]Corpus de Referencia del Español Actual (CREA)[END_REF] , expressed in occurrences per million words, while equivalent data for the EN dataset come from the SUBTLEX-UK corpus [START_REF] Van Heuven | SUBTLEX-UK: A new and improved word frequency database for British English[END_REF] , expressed in Zipfs. The Zipf scale is defined as log10 (frequency per billion words) and ranges from around 1 (very low frequency words) to 7 (extremely common words, mainly function words and pronouns). For example, in the current datasets, common words "por" and "we" have a Zipf value around 7 and the far less common words "bromeas" and "fifteenth" have values near to 2. The Zipf scale is argued to avoid the problem of interpreting negative values that arise from log-transformed counts per million words that occur when counts are derived from very large corpora 14 . To ease comparability in the current study, lexical frequencies in the SP dataset were derived by converting values to Zipfs. Mean word frequencies for the SP and EN datasets are very similar, at 4.23 (std. 0.70) and 4.20 (std. 0.81) Zipfs respectively.

Results

Lexical frequency differences

Lexical frequency differences were computed by subtracting the frequency of the target word from that of the misperception, so that positive lexical frequency differences correspond to misperceptions that are more common words.

Across masking conditions, mean lexical frequency differences for SP and EN are 0.39 and 0.44 Zipfs respectively, indicating that, on average, misperceptions are 2.5-2.75 times more common than target words. A breakdown by type of masker (Fig. 1) reveals that the lexical frequency difference originates largely in the pure energetic maskers (SSN, BMN1, BMN3); the two maskers with an informational component (BAB4, BAB8) show a much smaller lexical frequency effect. For example, on average, Spanish misperceptions reported To eliminate further possible confounds, we examined four factors that might have influenced the pattern of lexical frequency differences across masker types.

Words from the masker

Misperceptions in the EN and SP datasets occasionally correspond to complete words contained in the BAB4 masker. Since maskers were constructed from the same set of speech materials as the target words, a mean lexical frequency difference of zero is to be expected for these cases, leading to a potential source of bias. Such cases amount to some 316 tokens (around 5% of the combined datasets), of which 269 occur in the EN dataset. After excluding these cases, the lexical frequency difference for the BAB4 masker in EN increases from 0.18 to 0.31 Zipfs, while for SP the increase is more modest, from 0.09 to 0.12 Zipfs. However, a significant masker effect remains [F (2, 4806) = 47.1, p < .001, η 2 = 0.019], indicating that the occasional reporting of complete words from the babble might account for part of the limited lexical frequency effect in the EN dataset, but has almost no impact on the SP corpus.

Word length differences

Shorter words tend to be more common, and different maskers may result in different patterns of phoneme deletion. For example, the quasi-stationary SSN masker might be expected to leave more energetic target components near to syllable nuclei intact, while maskers with significant temporal modulation might produce a more uniform pattern of deletions across phonemes.

For the misperceptions of the current datasets, length in phonemes is indeed inverselyrelated to lexical frequency [EN: r = -0.38, SP: r = -0.30, both p < .001]. However, a significant masker effect remains, albeit with a reduced effect size, after excluding target/misperception pairs of differing phoneme length [F (2, 1999) = 21.2, p < .001, η 2 = 0.021].

Combining the equal-length criterion with exclusion of words from the masker (Section 3.1.1) leads to a further reduction in effect size [F (2, 1929) = 13.9, p < .001, η 2 = 0.014]. Interpretation of causality in the relationship between lexical frequency and word length is problematic [START_REF] Felty | Misperceptions of spoken words: Data from a random sample of American English words[END_REF] , since misperceptions may be shorter because they are of higher frequency.

Influence of extreme Zipf values

To check whether lexical frequency differences were influenced by extreme Zipf values, we examined the ratio of the number of target-misperception pairs with a positive lexical frequency difference to those with a negative lexical frequency difference, a metric that removes the influence of absolute frequency values. Across maskers, the ratio produces a clear bimodal pattern similar to that seen in Fig. 1. For example, about 2.8 times as many pairs have a positive difference for the SSN masker, a ratio that decreases to 1.3 for the BAB4 masker.

Duplicate target-misperception pairs

Due to the procedure used to generate new speech-in-noise tokens on demand during elicitation of the EN and SP datasets, which involved random selection of a target word from a base corpus, both datasets contain a number of duplicate target-misperception pairs (note that even though targets were presented multiple times, they may have come from different talkers and were mixed at varying SNRs with potentially different maskers). For instance, the target word 'perverse' (3.13 Zipfs) was misperceived as the more common word 'reverse' (4.15 Zipfs) on two occasions. A re-analysis limited to unique pairs only (counts of which are indicated in Table 1) produces a highly-similar pattern to that seen in Fig. 1 and a clear effect of masker type [F (2, 3945) = 70.0, p < .001, η 2 = 0.034], ruling out any influence from duplicate pairs.

Energetic masking

Although the lexical frequency differences observed in Fig. 1 vary across maskers, these differences might not stem from masker type per se but rather from differences in degree of energetic masking, which were not fixed or equalised across maskers (recall that SNR ranges were chosen to favour the elicitation of misperceptions for that masker type). As noted in the Introduction, one study 7 found that listeners were more likely to report words with a higher lexical frequency in noise at low SNRs. Our results also show a negative correlation between the size of the lexical frequency difference and SNR across maskers [SP: r = -0.15, EN: r = -0.12; both p < .001]. However, SNR is known to be a poor predictor of intelligibility when comparing maskers which vary in their spectro-temporal modulation properties [START_REF] Festen | Effects of fluctuating noise and interfering speech on the speechreception threshold for impaired and normal hearing[END_REF] . As an alternative proxy for pure energetic masking, glimpse percentages were computed for the two datasets (Fig. 2). Glimpse percentages have been shown to provide reasonable first-order predictions of intelligibility for a range of different speech and masker types [START_REF] Tang | Glimpse-based metrics for predicting speech intelligibility in additive noise conditions[END_REF] . for the ranges of SNRs used here. Moreover, glimpse percentage is lower for the three pure energetic maskers than for the two babble maskers, suggesting that part of the lexical frequency effect seen in Fig. 1 could be due to scarcity of information about the target that is predicted to survive masking. Nevertheless, energetic masking cannot entirely explain the across-masker disparity between lexical frequency differences. For example, BMN1 and BAB8 are both predicted to leave the target word occupying around 20-22% of the spectrotemporal plane, yet the BMN1 masker results in a far larger lexical frequency effect.

SSN

Discussion

In two extensive corpora, misperceptions reported by listeners were words of a higher lexical frequency than their corresponding intended target words. Lexical frequency difference shows an apparent dependence on the type of masker, being substantially larger for three pure energetic maskers than two babble maskers (Fig. 1), but some of the effect may be due to differences in the amount of acoustic information which survives masking according to a glimpsing model (Fig. 2). This outcome supports the finding of an increased lexical frequency effect at lower SNRs 7 . It is conceivable that increased acoustic uncertainty favours the use of word frequency priors. An example from the EN dataset illustrates this possibility: "clinic" with a lexical frequency of 3.9 Zipfs was misperceived as "finish" (5.1 Zipfs) in the presence of the SSN masker, perhaps due to the masker eroding acoustic-phonetic information for the target word apart from evidence for the two vowel nuclei, leaving listeners to hypothesise a word with the corresponding vowels. In such situations, one would anticipate lexical frequency having a role in the choice of word to report. If lexical frequency is more likely to come into play in more adverse masking conditions, the absence of a frequency effect for naturalistic word misperceptions 6 may be due to the environment under which mispercep-tions occurred being insufficiently adverse to engage prior lexical frequency information in the process of deciding which word was heard.

However, a comparison of Figs. 1 and 2 suggests that something more than pure energetic masking is needed to fully explain the role of lexical frequency in word misperceptions.

One possibility is that the additional acoustic-phonetic information contributed by an informational masker acts as a source of constraint on possible word hypotheses, which in turn limits or eliminates a role for lexical frequency. This notion can be illustrated with an example from the EN dataset: target word "wife" (5.2 Zipfs) was misperceived in BAB4 for the less frequent word "twice" (4.8 Zipfs); an inspection of the words making up the babble provides clear evidence for a word-initial /t/ and a word-final /s/ with a temporal alignment appropriate for their incorporation in the reported word. Here, the ability to fit alternative word candidates is constrained by elements in the babble, attenuating the influence of lexical frequency. The limited room for manouevre in the presence of additional phonetic cues contrasts with the uncertainty created in the face of missing information due to pure energetic masking. Further support for this hypothesis awaits a detailed examination of each individual misperception in the context of the acoustic information of the babble signal which elicited the misperception.

The reduced lexical frequency effect for our 4-and 8-talker babble maskers for SNRs below 0 dB is at odds with the findings of Felty et al. [START_REF] Felty | Misperceptions of spoken words: Data from a random sample of American English words[END_REF] , who reported a lexical frequency effect for a 6-talker babble masker for SNRs in the range 0-10 dB. However, there are differences in both the speech and masker materials and the elicitation techniques used in the two studies.

Perhaps the biggest disparity is in the mean lexical frequency of the target words. Using the US subtitle-based lexical frequency data [START_REF] Brysbaert | Moving beyond Kucera and Francis: A critical evaluation of current word frequency norms and the introduction of a new and improved word frequency measure for American English[END_REF] , we calculated the mean Zipf value for the target words of Felty et al. to be 3.16 Zipfs, a value substantially lower than the mean of around 4.2 Zipfs for the datasets of the current study. Since low frequency targets are a priori more likely to result in higher frequency responses than targets of a higher mean lexical frequency, it is understandable that Felty et al. [START_REF] Felty | Misperceptions of spoken words: Data from a random sample of American English words[END_REF] observed a lexical frequency effect at higher SNRs than those used in the current study. A further difference between the two studies is the nature of the speech material making up the babble. In Felty et al. [START_REF] Felty | Misperceptions of spoken words: Data from a random sample of American English words[END_REF] the masking material came from a different talker than that of the target words, while in the current study the target talker could also appear in the babble. Informational masking effects are thus expected to be higher for our stimuli, and as a consequence it seems likely that speech fragments from the masker were more easily misallocated into the final word misperception.

The structure of English and Spanish differs in many respects, including vowel inventory size (greater for EN), inflectional morphology (richer for SP), and presence of consonant clusters (greater for EN). In spite of these differences, the similar across-masker patterning of lexical frequency effects for the two languages suggests that relatively low-level processes such as energetic masking and misallocation of acoustic-phonetic evidence from the masker can modulate the extent to which lexical frequency priors are engaged during word recognition.

Conclusions

Across five types of masker and two languages, listeners reported words of a higher lexical frequency than the intended target words. The size of the lexical frequency effect was larger for pure energetic maskers than for maskers containing speech. However, the pure energetic maskers of the current study possessed a greater predicted masking potential than the babble maskers, suggesting that lexical frequency has more influence when acousticphonetic information is scarce. The role of lexical frequency might be reduced in the presence of a speech-based masker, by limiting the number of lexical hypotheses compatible with audible acoustic-phonetic evidence from both target and masker.

Fig. 1 .

 1 Fig. 1. Mean lexical frequency differences for each masker and dataset. Error bars indicate ±1

Fig. 2 .

 2 Fig. 2. Mean glimpse percentages for each dataset and masker combination. Glimpse percentage

Table 1 .

 1 Misperception counts for the Spanish (SP) and English (EN) datasets in each masking condition, alongside statistics of the SNRs used during their elicitation, which varied within the range shown. 'Unique' refers to counts after removing duplicates (see section 3.1).

				Counts		SNRs (dB)
	Masker	Dataset	Total	Unique	mean	std.	min	max
	SSN	SP	609	437	-5.4	0.9	-7.0	-4.0
		EN	1068	759	-5.5	0.9	-7.0	-4.0
	BMN3	SP	732	533	-5.3	1.4	-7.9	-3.0
		EN	1196	903	-5.5	1.4	-8.0	-3.0
	BMN1	SP	777	611	-9.9	1.8	-13.0	-7.0
	BAB8	SP	419	345	-1.2	1.3	-4.0	1.0
	BAB4	SP	589	501	-0.9	1.2	-3.0	1.0
		EN	934	818	-1.2	1.2	-3.0	1.0

Acknowledgments

This work received support from the Basque Government under grant Language and Speech (IT311-10).