Nicolas Grenier

Marie-Christine Duluc

Patric Mantaropoulos

Florine Giraud

Brice Tremeac

Pascal Tobaly

Numerical Simulation of Bubble Growth Under Low Pressure

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

Phase change is a complex phenomenon involving multi-physics and multi-parameters and is more complex at low pressure since the hydrostatic pressure can no longer be neglected compared to the interface pressure. In these conditions a boiling bubble can grow up to 15 centimetres in height and be subjected to very heterogeneous conditions on its interface which affects bubble shape and growth. Many other parameters (pressure, temperature, etc.) could impact bubble along its lifetime and are difficult to control in experiments.

We propose to use direct numerical solver to give some insights while simplifying the problem. An in-house two-fluids compressible solver based on an accurate low-Mach numerical scheme [START_REF] Grenier | An accurate low-Mach scheme for a compressible two-fluid model applied to free-surface flows[END_REF] will be employed to consider hydrodynamical aspect of bubble growth.

First we will consider the dilatation of an isothermal gas inclusion at low pressure under a free-surface. Good qualitative reproducibility of experimental results (with phase change, ignored in simulations) will be shown.

Then phase change model build on instantaneous thermodynamical and mechanical relaxation [START_REF] Faccanoni | Modelling and numerical simulation of liquid-vapor phase transition[END_REF] will be added. Influence of this model on bubble growth will be assessed against experimental results.

  . Grenier 1 * , M.-C. Duluc 2,3 , P. Mantaropoulos 3 , F. Giraud 3 , B. Tréméac 3 and P. Tobaly 3In the context of global warming, working fluids of air conditioners or heat pumps are harmful for climate and active research is ongoing to find replacement solutions. A potential candidate is to use water as working fluid. But to evaporate at ambient temperature at which air conditioners operate working pressure must be very low, around hundredth of atmospheric pressure. Apart from mechanical design and processing issues at this subatmospheric pressure, these heat exchangers experience inefficiency due to the lack of understanding of boiling phenomena at low pressure as usual correlations at atmospheric pressure are no more valid. Experimental studies are scarce while numerical simulations are inexistent on the subject to help build new correlations.

	14th World Congress on Computational Mechanics (WCCM)
	ECCOMAS Congress 2020
	19-24 July 2020, Paris, France
	NUMERICAL SIMULATION OF BUBBLE GROWTH UNDER LOW
	PRESSURE
	1 Université Paris Saclay, CNRS, LIMSI, Orsay, France, grenier@limsi.fr
	2 Université Paris Saclay, CNRS, LIMSI, Orsay, France, duluc@limsi.fr
	3 CNAM, Paris, France
	Key Words: DNS, two-phase flows, low-Mach, low pressure, phase change, evaporation, bubble, heat
	exchanger.

N


Ziqiang Zou

Nicolas Grenier

Christian Tenaud

Samuel Kokh

A stable sharp interface low-mach scheme for two-phase dilatable flows

14th World Congress on Computational Mechanics (WCCM) ECCOMAS Congress 2020 19-24 July 2020, Paris, France

A STABLE SHARP INTERFACE LOW-MACH SCHEME FOR TWO-PHASE DILATABLE FLOWS

Ziqiang Zou 1 , Nicolas Grenier 2 , Christian Tenaud 2 , Samuel Kokh 3 and Edouard Audit 1

1 Université Paris-Saclay, UVSQ, Inria, CNRS, CEA, Maison de la Simulation, 91191, Gif-sur-Yvette, France. 2 Université Paris-Saclay, CNRS, LIMSI, 91400, Orsay, France. 3 Université Paris-Saclay, CEA, Service de thermo-hydraulique et de mcanique des fluides, 91191, Gif-sur-Yvette, France.

Key Words: Low-Mach correction, sharp interface, scheme stability, Level-Set, Ghost Fluid method, surface tension, phase transition Two-phase non-miscible flows with phase transition are often encountered in a wide range of industrial processes such as cooling and heat exchangers, an accurate and stable numerical solver is then necessary to predict the behavior of fluids. Flows of interest contain one liquid phase and one gas phase separated by an interface. The interface is of shock wave type discontinuity without mixture and remains sharp.

The retained method to predict the interface motion is the Level-Set method [1].

Although in the liquid phase the Mach number is generally very low, each phase of the two-phase flow is described by a compressible solver called all regime Lagrange-Projection like numerical scheme. The main object is to deal with dilatable flows mainly in the gas phase and the key idea is to decouple the acoustic and transport phenomenon and then alter the numerical flux in the acoustic approximation to obtain a uniform truncation error in terms of Mach number [2]. According to the acoustic subsystem, an approximate Riemann solution that accounts for the capillary effects and phase transition is considered. The surface tension is treated as a pressure jump condition at interface with a well-balanced scheme, while the mass transfer is treated as the normal velocity jump across the interface. Based on net energy transfer across the interface, we can derive the mass transfer rate and determine the velocity jump [3].

To avoid mixing cell and remain interface sharp, the Ghost Fluid strategy [4] is applied for the coupling at interface.

When the fluid motion velocity is small compared to the sound speed, the low-Mach correction is necessary to keep the accuracy of a Godunov type Riemann solver. The ratio of pressure perturbation magnitude between two different phases could be extremely high, as the fluid property could vary a lot across the sharp interface. Classical low-Mach schemes [5][6] suffer from some problems of destabilization with the presence of high density and sound speed ratio across the interface. In this work, we propose a new stable low-Mach correction that takes density ratio into account and gives a stable prediction with suitable CFL condition. Numerical results on classical test-cases will be given at the conference and show the capability and efficiency of the proposed new approach.

E-mail: ziqiang.zou@cea.fr


Maëva Garnier
email: maeva.garnier@gipsa-lab.fr

Eric Le Ferrand
email: eric.le-ferrand@univ-grenoble-alpes.fr

Fabien Ringeval
email: fabien.ringeval@imag.fr

Verbal and nonverbal feedback signals in response to increasing levels of miscommunication

Keywords: conversational dynamics, backchannels, feedback, repair, multimodality, verbal and nonverbal communication

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

When listeners have difficulty hearing or understanding their interlocutor, they typically use a set of conversational strategies [START_REF] Axelsson | Multimodal user feedback during adaptive robot-human presentations[END_REF] to request a repetition [START_REF] Curl | Practices in other-initiated repair resolution: The phonetic differentiation of'repetitions[END_REF], correction [START_REF] Bolden | Speaking 'out of turn': Epistemics in action in other-initiated repair[END_REF], or clarification of what was said [START_REF] Dingemanse | Other-initiated repair across languages: towards a typology of conversational structures[END_REF][START_REF] Purver | The theory and use of clarification requests in dialogue[END_REF]. These repair initiators can take different linguistic forms, ranging from short non-lexical sounds ("hmm?") to simple words ("sorry?") or sentences ("what did you say?") [START_REF] Ward | Non-lexical conversational sounds in american english[END_REF][START_REF] Young | Identifying units in interaction: Reactive tokens in korean and english conversations[END_REF]. They can also vary in their level of specificity, from open repairs that do not specify what or where the problem is ("what?"), to restricted repairs ("when?") that specify which part of the utterance needs to be clarified, and restricted suggestions that indicate even more specifically what element was misunderstood, and offer suggestions for it ("did you say tomorrow?") [START_REF] Dingemanse | Universal principles in the repair of communication problems[END_REF][START_REF] Fusaroli | Measures and mechanisms of common ground: Backchannels, conversational repair, and interactive alignment in free and task-oriented social interactions[END_REF]. Finally, like other types of backchannels, these repair initiators are multimodal, and verbal expressions have been shown to be accompanied by prosodic patterns [START_REF] Kendrick | Other-initiated repair in english[END_REF], movements of the body or head, such as leaning forward or turning towards [START_REF] Dingemanse | A coding scheme for other-initiated repair across languages[END_REF][START_REF] Heylen | Challenges ahead: Head movements and other social acts in conversations[END_REF], and facial expressions [START_REF] Oloff | sorry?"/"como?"/"was?"-open class and embodied repair initiators in international workplace interactions[END_REF]. Previous studies have shown that the frequency and form of these repair initiators depend on the communication context. Thus, repair is more frequent in task-oriented conversations, compared to spontaneous interactions [START_REF] Colman | The distribution of repair in dialogue[END_REF], and contexts requiring precision involve more specific forms of repair [START_REF] Fusaroli | Measures and mechanisms of common ground: Backchannels, conversational repair, and interactive alignment in free and task-oriented social interactions[END_REF]. Recent work has also shown that listeners use specific feedback to indicate the nature of their impairments, in particular to distinguish between hearing impairments (e. g. , lifted eyebrows) and comprehension impairments (e. g. , facial freeze) [START_REF] Oloff | sorry?"/"como?"/"was?"-open class and embodied repair initiators in international workplace interactions[END_REF].

The purpose of this study is to further explore the multi-modality of these repair initiators, specifically facial expressions, head movements, and gaze, which listeners may use to indicate that they are experiencing hearing or comprehension difficulties in task-oriented dialogues. Since these visible manifestations may be shared with other backchannels or communicative attitudes [START_REF] Bavelas | Gestures specialized for dialogue[END_REF], we sought to disentangle these different aspects by exploring: 1-whether certain nonverbal cues are particularly synchronized with the instant of communication disruption, and 2-whether the magnitude of certain cues correlates with an increasing level of miscommunication, or whether they are used specifically to indicate a certain level of miscommunication.

C1 C2 C3

You

Material and Method

Participants and experimental setup

Fifteen participants (seven females and eight males, ages 20-60), were recorded while playing a map task with a partner. Both players were in two separate rooms and communicated through a special video conferencing system that allowed them to look at each other as if in a natural face-to-face interaction situation. Sound was recorded with a headset microphone. Participants played the role of follower in the map task, while one of the experimenters, posing as another participant, always played the role of leader. The different maps of the game were displayed and filled in by participants, using a graphics tablet, whose screen was duplicated to also be displayed to the leader. An electronic device equipped with a push button was inserted at the output of the leader's auvio-visual stream, to simulate random disruptions of the transmission by interrupting the signals sent to the participant when the button was pressed, producing a black screen and audio silence.

Although the interaction seemed spontaneous, the game was in fact entirely scripted. First of all, the instructions for the map task, given by the leader, were written in advance, and were all built on the same model, made of three components (cf. Figure 1):

• C1: You + non-specific verb of movement ("go", "pass", "should go") • C2: Preposition of place ("to the left of", "to the right of", "above", "below") • C3: Monosyllabic word designating an object of the map ("the chair", "the key", . . . )

Transmission disruptions were triggered by the leader at very specific times in order to mask a component (either C1, C2, or C3) of the leading instructions (cf. Figure 1). The whole scenario was designed so that the disruptions appeared to occur randomly, but in the end, we obtained an equal number (N=12) of instructions that fell into one of the following categories:

• NP: instruction without any perturbation.

• P0: instruction with a missing onset, which was expected to cause hearing difficulty, but did not impact overall comprehension. • P1: instruction with a missing place preposition, which was expected to have a moderate impact on comprehension, without completely preventing the tracing of a path. • P2: instruction with a missing target, which was expected to have a severe impact on comprehension and, in the absence of clarification, prevent completion of the task.

After a first session of the map task in remote interaction, a second session was recorded, in which the participant again received audiovisual instructions from the map task leader. However, in return, his/her own audio-visual signals could no longer be transmitted to the leader, making the communication onesided and non-interactive.

Data labeling and analysis

The audio and video signals of both the map task leader and the participants were recorded synchronously. The leader's instructions were manually annotated, using Praat software [START_REF] Boersma | Praat: doing phonetics by computer[END_REF]. All participants' verbal and nonverbal expressions were labelled manually and freely, using ELAN software [START_REF] Brugman | Annotating multimedia/multi-modal resources with elan[END_REF]. This also enabled us to verify that all the undisrupted instructions (NP) were indeed well understood. We measured the frequency of each category of feedback signal across the eight conditions -i. e. , {NP, P0, P1, P2} x {interactive, non-interactive situations} -, their average onset time after the start of each leader instruction, and, for facial expressions, the degree of Facial Action Units (FAU) activation that was automatically estimated using OpenFace software [START_REF] Baltrusaitis | Openface 2.0: Facial behavior analysis toolkit[END_REF]. Statistical analyses were performed using R software, considering mixed models with Interaction and Disruption position as fixed factors, and a random effect on the participant.

Results and discussion

Categorization of the observed signals

Fifty multimodal feedback signals were identified from the annotations, including sixteen acoustic or verbal signals that have been grouped into the six following categories:

• Confirmation marks: non-lexical sounds (e. g. , "hmm"), small affirmative words (e. g. , "yeah", "ok", "all good", . . . ), or an affirmative repetition of the previous utterance. • Hesitation marks: non-lexical sounds (e. g. , "uuh") and small phrases (e. g. , "Dunno . . . ")

• Open repair initiators: small interrogative words (e. g. , "what?", "sorry?"), sentences to tell a problem (e. g. , "There are breakdowns"), a hearing or comprehension difficulty (e. g. , "I didn't hear you"), or request repetition of the instruction (e. g. , "Can you repeat that?") • Restricted repair initiators: small interrogative words ("where?"), repetitions of part of the instruction, with an invitation to complete a misunderstood part (e.g. "I need to go to the right of . . . ?"), or sentences to indicate what was not understood (e.g. "I didn't hear the end of your sentence") • Restricted suggestions: repetition of the utterance with a focused, interrogative suggestion in place of the disrupted constituent (e.g. "Should I go to the left of the dress ?") 3). Two nonverbal signals: "Horizontal nod" and "Smile", followed the same pattern and were also observed with a sig-

Participants (%)

Eyebrow frowning

Interaction No interaction Interaction No interaction

Horizontal nod

Interaction No interaction

Eyebrow raising

NS NS

Interaction

No interaction

Smile

Interaction No interaction nificant frequency in the interactive condition only (cf. Figure 3 (bottom)). We can therefore consider these eight behaviors as communicative signals deliberately addressed to the interlocutor. Among them, we observed, as expected, that small confirmation words (e. g. , "ok", "yeah", . . . ) and affirmative repetitions of the instruction were produced only following undisrupted instructions (NP) or disrupted instructions that can still be understood (P0). We can therefore consider them as marks of understanding and task completion. Conversely, we can also consider as a mark of incomprehension the absence of these confirmation signs after moderately and severly disrupted instructions (P1, P2).

Inverted smile

Interaction

In contrast, the other four verbal signals "Telling a problem", "Question-where", "Partial repetition" and "Suggestion", and the two nonverbal signals "Horizontal nod" and "Smile" were observed with significant frequency in the two perturbed conditions P1 and P2 only, in which participants lacked information to complete the task and needed misunderstood instructions to be repaired (cf. bottom of Figure 3). These six signals can therefore be considered as repair initiators deliberately addressed to the interlocutor. The fact that none of these signals were also observed in P0 (in addition to P1 and P2), shows that individuals do not (or rarely) express their hearing difficulty until it actually affects their comprehension. Interestingly, the verbal signal "Partial repetition" and the nonverbal signal "Smile" had their frequency significantly increased by the degree of disruption (P2 vs. P1: respectively +35.1 ± 7.5%, p < .0001 ; +9.1 ± 4.1%, p = 0.028). We also observed that the two nonverbal signals "Horizontal nod" and "Smile" were rarely observed alone, but almost always with verbal signals (93% and 81% of the time, respectively), suggesting that they may be accompanying signals, rather than being repair initiors per se.

On the other hand, two nonverbal signals: "Eyebrow raising" and "Making eye contact" were observed in both interactive and non-interactive conditions, although with a significantly higher frequency without interaction (cf. Figure 3). This means that these signals are not deliberate communication signals addressed to the interlocutor. Instead, they may rather reflect the listener's cognitive and emotional state [START_REF] Ringeval | Introducing the RECOLA Multimodal Corpus of Remote Collaborative and Affective Interactions[END_REF][START_REF] Kossaifi | SEWA DB: A Rich Database for Audio-Visual Emotion and Sentiment Research in the Wild[END_REF], such as surprise, hesitation, disturbance, reflection. Thus, "Eyebrow raising", was observed 46% of the time without a co-occuring verbal signal, with a significant frequency for incomprehensible utterances only (P1, P2). "Making eye contact", however, occured for both disrupted and undisrupted instructions (cf. Figure 3), with a comparable frequency of occurence in the non-interactive situation, but with an increased frequency for incomprehensible utterances (P1, P2), compared to undisrupted and mildly disrupted utterances (SP, P0) in the interactive situation.

Finally, two nonverbal signals : "Eyebrow frowning" and "Inverted smile" were observed with a significant frequency in the non-interactive situation only (cf. bottom of Figure 3), rarely with a co-occuring verbal signal, and for moderate and severe degrees of miscommunication (P1 and P2). It turns out that the task was difficult or impossible to perform in these two specific conditions, due to the fact that no repair could be provided by the leader for the misunderstood instructions in the non-interactive situation. It is therefore possible that these two signals reflect the participant's sense of inability to complete the task.

Timing of the feedback signals

As expected, participants' verbal signals were observed after the leader's instruction ended (about 1 s later, on average), with little effect of the degree of miscommunication on their onset time (cf. Figure 4). Contrary to our expectations, nonverbal signals (including "Making eye contact") were not produced immediately after the disruption, during the leader's instruction, but also after the end of the instruction, in a similar or even later time frame than verbal signals. Thus, "Horizontal nods" not only almost always occured with verbal signals, as described in the previous section, but also synchronously with them. This supports further that they may have the same function and meaning as the verbal repair initiators they accompany.

Despite a high percentage of co-occurence with the verbal signals, the "Smiles", however, were produced about 1s later, supporting the idea that they may have a different communicative function. Finally, in the interacive situation, the eye contact initiation times showed a bimodal distribution after a disrupted utterance (cf. Figure 5): a first peak was observed about 1 s after the end of the leader's instruction, i. e. , within a similar time frame as "Horizontal nods" and verbal responses (cf. Figure 4), and thus probably expressing listener uncertainty or misunderstanding; a second late peak was observed between 2 s and 8 s after the end of the instruction, with a delay that increased with the degree of miscommunication (NP → P0 → P1 → P2). In this case, "Making eye contact" seems to correspond rather to the completion of the task (immediately, or after the repair of the utterance), and could be considered as a turn-taking signal to invite the leader to deliver the next instruction [START_REF] Krahmer | The dual of denial: Two uses of disconfirmations in dialogue and their prosodic correlates[END_REF]. In the non-interactive situation, on the contrary, a single late peak was observed in the distribution of eye contact initiation times, following a disrupted instruction. Coupled with the fact that the cumulated eye contact duration was also significantly greater in the non-interactive situation than in the interactive situation (+29.4 ± 14.6%, p = 0.04), this may indicate that the main function of eye contact in the non-interactive condition is to retrieve visual information in order to better understand speech, especially when disruptions may occur and perturb this understanding. "Making eye contact" in the non-interactive situation could therefore indicate that the listener is ready to receive the next instruction [START_REF] Krahmer | The dual of denial: Two uses of disconfirmations in dialogue and their prosodic correlates[END_REF]. The second additional peak observed in an undisrupted situation (NP), approximately 3 s after the first eye contact initiation, could reflect a form of impatience or surprise that the leader has not given yet the next instruction.

Amplitude of facial movements

Only two feedback signals showed a significant increase in the activation of their corresponding FAU from a moderate (P1) to a severe (P2) level of miscommunication: "Eyebrow frowning" (+0.54±0.15, p = .0006) and "Inverted smile" (+0.55±0.23, p = .029).

Conclusions

We showed that listeners produce a set of verbal and nonverbal feedback signals in task-oriented conversations, all of which occur after the end of the received instruction, rather than immediately after the disruption, and only after moderate to se- vere levels of disruptions. They therefore appear to be related to task success or failure, rather than to "sensory disruption". Nevertheless, some differences were observed in the frequency, timing or magnitude of these signals between moderate and severe levels of miscommunication : for example, "Partial repetitions" and "Smiles" were more frequent, "Making eye contact" occured later, and "Eyebrow frowning" and "Inverted smiles" were more pronounced after severe disruptions. Moreover, based on their different contextual use, i. e. , either in interactive situations only, in non-interactive situations only, or both, and according to their timing and co-occurence, these different signals seem to convey different functions and meanings: some of them, like "Eyebrow raising", "Eyebrow frowning", or "Inverted smile" do not seem to be deliberately addressed to the interlocutor. Rather, they seem to be personal reactions of uncertainty, incomprehension, or inability to complete the task. Others, such as verbal signals, "Horizontal nods", "Smiles", or "Making eye contact" that immediately follow disrupted utterances, can be considered as repair initiators, i. e. , communicative signals deliberately addressed to the interlocutor to ask for repetition or clarification. Finally, "Making eye contact" seems to have multiple functions: when it occurs a few seconds after the end of the leader's instruction, it rather seems to indicate that the task has been correctly accomplished, or that the listener is ready and waiting for the next instruction (turn-taking signal). These different feedback signals and usages were observed here for task-oriented conversations. Further exploration would be needed to extend and/or complement these observations to other types of dialogues, such as those observed in the context of health care [START_REF] Tarpin-Bernard | THERADIA: Digital Therapies Augmented by Artificial Intelligence[END_REF].

Figure 1 :

 1 Figure 1: Example of an interaction map (left) with the instructions the leader could give (right), and the perturbations (P0, P1, and P2) that could occur either on the first (C1), second (C2), or third (C3) component of the utterance, leading to increasing levels of miscommunication.

E y e s s q u i n t i n g L o o k i n g u p o r s i d e w a y s T e l l i n g p r o b l e mFigure 2 :

 2 Figure 2: Verbal and nonverbal feedback signals, ranked by decreasing percentage of participants who showed them.

Figure 3 :

 3 Figure 3: Percentage of instructions for which the different verbal and nonverbal feedback signals were observed, in either interactive or non-interactive conditions, in an undisrupted situation (NP) or for increasing levels of miscommunication (P0, P1, P2).

Figure 4 :

 4 Figure 4: Average delay of appearance of verbal and nonverbal feedback signals, from the onset of the leader's instruction.

«Figure 5 :

 5 Figure 5: Distribution of the eye contact initiation times, relative to the onset of the leader's instruction, for disrupted and undisrupted instructions received in either the interactive or non-interactive condition.

  • Brief signal whose meaning is less clear, nor if they are really addressed to the interlocutor: non-lexical sounds (e. g. , laughter, loud breath, sigh), and swearing.

	The thirty-four remaining signals are all nonverbal and have
	been classified into four categories, based on the facial region
	involved and Ekman's system of facial actions coding [19]:
	• Head: vertical (up-down) and horizontal (left-right) nodding,
	rocking (left-right tilt), sudden forward or back movement, or
	rotation to one side.

• Upper face: Making eye contact, squaring, squinting or voluntary closing of the eyes, looking up or sideways, frowning of one or both eyebrows, raising of one or both outer eyebrows (as in a frightened or surprised face), or raising of the inner eyebrows (as in a sad or sorry face). • Lower face: spontaneous or artificial smile (lip corners raised), lip spreading on one or both sides (straight lip corners), "inverted" smile (lip corners depressed + chin raised), lip compression in the middle or on one side, "pout" (compression + slight forward movement) in the middle or on one side, lip protrusion (closed), frowning of the chin, dropping of the jaw with closed or open lips, lowering of the nasolabial region, raising of the upper lip (with open lips). • Other communicative behaviors: finger on the lips or chin, raising the shoulders, touching one's ear. 3.2. Frequency of the feedback signals according to the type of interaction, and the level of miscommunication Twelve feedback signals (six verbal, and six nonverbal) were observed in more than half of the participants (cf. Figure 2). On one hand, the six most common verbal signals were observed almost exclusively in the interactive condition (cf. top of Figure

Acknowledgements

This project was supported by a local grant of the Pole Grenoble Cognition. We thank Frederic Elisei and Xavier Laval for their help with the experimental setup.


Etienne Boncourt

Björn Reineking

Gabriel Chambonnet

Stéphanie Gaucherand

Gaucherand

Stéphanie

Movement behaviour of the common frog (Rana temporaria) in an anthropized mountain landscape: integrated step selection analysis of GPS tracking data

Keywords: ski resort, movement ecology, Step Selection Function SSF, mountain ecology, ski run

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

movements between breeding, foraging and overwintering habitats. Understanding how amphibians move across a landscape is a key component to improving their conservation [START_REF] Pittman | Movement ecology of amphibians: A missing component for understanding population declines[END_REF].

Frog movement has been studied for decades, initially by tagging animals (e.g. Breder, Breder and Redmond, 1923;[START_REF] Martof | Home Range and Movements of the Green Frog, Rana Clamitans[END_REF], then by VHF tracking since the 1960s [START_REF] Kays | Terrestrial animal tracking as an eye on life and planet[END_REF]. These techniques allowed the study of animal movement patterns such as homing (Breder, Breder and Redmond, 1923;[START_REF] Matthews | Response of Mountain Yellow-Legged Frogs, Rana muscosa, to Short Distance Translocation[END_REF][START_REF] Mazerolle | Landscape resistance to frog movements[END_REF], home range extent [START_REF] Martof | Home Range and Movements of the Green Frog, Rana Clamitans[END_REF] and habitat selection [START_REF] Groff | Evaluation of a waistband for attaching external radiotransmitters to anurans: Attaching Radiotransmitters to Anurans[END_REF][START_REF] Groff | Hibernal Habitat Selection by Wood Frogs (Lithobates sylvaticus) in a Northern New England Montane Landscape[END_REF].

Habitat selection by animals is traditionally assessed by comparing point observation data either to the total proportion of the considered habitat in the study area or to randomly chosen locations in the area (e.g. [START_REF] Groff | Hibernal Habitat Selection by Wood Frogs (Lithobates sylvaticus) in a Northern New England Montane Landscape[END_REF].

In recent years, the advent of GPS technology has provided new opportunities for animal tracking. In particular, the ability to obtain fixes with a constant time interval and high temporal and spatial resolution [START_REF] Cagnacci | Animal ecology meets GPS-based radiotelemetry: a perfect storm of opportunities and challenges[END_REF][START_REF] Hebblewhite | Distinguishing technology from biology: a critical review of the use of GPS telemetry data in ecology[END_REF][START_REF] Christensen | Use of GPS loggers to enhance radiotracking studies of semi-aquatic freshwater turtles[END_REF][START_REF] Kays | Terrestrial animal tracking as an eye on life and planet[END_REF][START_REF] Latham | The GPS craze: six questions to address before deciding to deploy GPS technology on wildlife[END_REF] allows the use of new statistical tools such as step selection functions (SSF, Fortin et al. 2005, Thurfjell, Ciuti and[START_REF] Thurfjell | Applications of step-selection functions in ecology and conservation[END_REF]. SSF allow the study of habitat selection considering steps instead of point observations [START_REF] Thurfjell | Applications of step-selection functions in ecology and conservation[END_REF].

Habitat use and availability are considered at a local scale [START_REF] Fortin | Wolves influence elk movements: behavior shapes a trophic cascade in Yellowstone National Park[END_REF].

Alpine ecosystems are important for biodiversity but are sensitive to human development, in particular to the development of tourism infrastructure [START_REF] Strong | Effects of mountain resorts on wildlife[END_REF][START_REF] Lassen | Ecoregion Conservation Plan for the Alps[END_REF][START_REF] Sato | The Effects of Winter Recreation on Alpine and Subalpine Fauna: A Systematic Review and Meta-Analysis[END_REF], but also to global warming, pollution, overgrazing, water abstraction or the introduction of alien species (Schmeller et al., 2022). Ski resort management alters vegetation, particularly on ski runs [START_REF] Kubota | Effects of ski resort management on vegetation[END_REF], and thus alters animal habitat [START_REF] Sato | The Effects of Winter Recreation on Alpine and Subalpine Fauna: A Systematic Review and Meta-Analysis[END_REF]. Despite this, little is known about the potential effects of human winter recreation infrastructure on amphibians [START_REF] Sato | The Effects of Winter Recreation on Alpine and Subalpine Fauna: A Systematic Review and Meta-Analysis[END_REF].

In this study, we used GPS technology to track the movements of amphibians in a ski resort. Our biological model was the European common frog Rana temporaria Linnaeus 1758. This species is widespread in Europe, extending beyond the Arctic Circle, and displays several adaptive traits to the mountain environment [START_REF] Beattie | The reproductive biology of common frog (Rana temporaria) populations from different altitudes in northern England[END_REF]Ryser, 1996, Miaud, Guyetant and[START_REF] Miaud | Variations in life-history traits in the common frog Rana temporaria (Amphibia: Anura): a literature review and new data from the French Alps[END_REF]. It is also known to be sensitive to changes in the landscape matrix [START_REF] Hitchings | Genetic substructuring as a result of barriers to gene flow in urban Rana temporaria (common frog) populations: implications for biodiversity conservation[END_REF][START_REF] Johansson | The influence of landscape structure on occurrence, abundance and genetic diversity of the common frog, Rana temporaria[END_REF][START_REF] Vos | Matrix permeability of agricultural landscapes: an analysis of movements of the common frog (Rana temporaria)[END_REF][START_REF] Decout | Integrative approach for landscapebased graph connectivity analysis: a case study with the common frog (Rana temporaria) in human-dominated landscapes[END_REF]. It is therefore an excellent model species for studying how frogs move through different land covers in a human-modified mountain landscape.

The study area was located on the snow front of the Les Arcs 2000 ski resort in the department of Savoie, France (GPS coordinates: 45.569 N 6.833 E, see Supplementary Figure S1). The elevation ranged from 2050 m to 2300 m a.s.l. The landscape consisted of several features, with lowland wetlands fed by small streams and roads that traversed the landscape. The wetland was a peatland characterised by hygrophilous herbaceous vegetation (e.g. Carex sp.). The soil was waterlogged, but there was no pond or other open water. All these elements were embedded in a matrix of grassland. Shrubs and trees were absent due to human intervention.

The fieldwork took place between July and August 2017. We captured 30 frogs in the wetlands at the lowest parts of the study area using landing nets during the day and at night. We fitted them with Gipsy-5 GPS tags from TechnoSmart. As these tags do not have a remote download system, we also fitted them with radio tags (Advanced Telemetry Systems, R1605 series glue-on transmitters) in order to recover the GPS tags (Supplementary Figure S2). The GPS tags were marinized by the manufacturer with heat-shrink tubes. The radio tags were already marinized. We glued the radio tag to the GPS tag and used the technique developed by [START_REF] Groff | Evaluation of a waistband for attaching external radiotransmitters to anurans: Attaching Radiotransmitters to Anurans[END_REF] to attach them to the frogs with a waistband, as this technique was described as safe for the animals based on tests with tags weighing up to 3.8 g or 9.3% of body mass. In our study, the mean weight of the frogs was 41.0 ± 7.7 g (median = 39.9 g) so the 4.4 g tags (GPS + VHF tags) represented 10.7% of the mean body mass of the tagged animals, slightly higher than the target of 10%. The tags were programmed to record a fix every 4 hours.

Fieldwork was conducted in summer to monitor daily movements rather than migration events, as this species is known to migrate in spring and autumn. Frogs do not move much during this period [START_REF] Pittman | Movement ecology of amphibians: A missing component for understanding population declines[END_REF]. To increase the likelihood of observing movement and associated habitat selection, we released the animals at different distances from their capture points, expecting them to return to their initial position, as homing is a well-documented behaviour in amphibians (Breder, Breder and Redmond, 1923;[START_REF] Matthews | Response of Mountain Yellow-Legged Frogs, Rana muscosa, to Short Distance Translocation[END_REF][START_REF] Mazerolle | Landscape resistance to frog movements[END_REF]. Capture-release distances ranged from 21 m to 521 m (supplementary Figure S1, supplementary material S3). We deliberately chose short distances in order not to exceed the movement capacity of this species (for example, the maximum migration distance is approximately 3,000 m, [START_REF] Decout | Integrative approach for landscapebased graph connectivity analysis: a case study with the common frog (Rana temporaria) in human-dominated landscapes[END_REF].

We obtained movement data for 20 out of 30 frogs (13 males, 5 females, 2 undetermined). Ten others could not be used (frogs lost tags too quickly, tags malfunctioned, not enough fixes, etc.). We recorded a total of 456 fixes (264 for males, i.e. 20.3 per male; 177 for females, i.e. 35.4 per female; 15 undetermined, i.e. 7.5 fixes per unsexed frog), which corresponds to 22.8 ± 25.4 fixes per individual (median = 12.5) over a period of 11.2 ± 6.3 days (median = 12.2). We assumed that the difference in the number of fixes recorded between males and females was due to chance (the moment the tag detached) and not to any biological difference. We recovered 100% of the tags.

We created a land use raster combining aerial photo interpretation from the 2013 BD ORTHO database with 0.5 m resolution provided by the Institut Géographique National (IGNdownloadable at http://geoservices.ign.fr/bdortho#telechargementanc) and field observations. We used five land use classes: grassland, wetlands, watercourses, ski runs and roads. We created a watercourse class by applying a 3 m buffer around the watercourses we observed in the field. This class thus included both the watercourses and their banks. We also used a 2016 digital elevation model with 5 m resolution from the BD TOPO of the IGN (downloadable at https://geoservices.ign.fr/bdtopo#telechargement2016) from which we calculated slope. We used hourly rainfall and temperature data from the Tignes meteorological station (GPS coordinates 45.467 N 6.907 E, altitude 2084 m, distance from the study area ~13 km) provided by MeteoFrance (https://donneespubliques.meteofrance.fr/?fond=produit&id_produit=110&id_rubrique=37).

We used integrated step selection functions (iSSF, [START_REF] Avgar | Integrated step selection analysis: bridging the gap between resource selection and animal movement[END_REF] to analyse how landscape and weather covariates influence common frog movement. iSSF allow for a detailed analysis of the effect of habitat on animal movements. They are an extension of step selection functions (SSF, [START_REF] Fortin | Wolves influence elk movements: behavior shapes a trophic cascade in Yellowstone National Park[END_REF] and compare each observed step (straight line between two successive locations with a constant time interval) with randomly generated steps considered as available to the animal. We considered as available all locations reachable in a step according to the distribution of all step lengths in any direction.

iSSF then typically use conditional logistic regression approach to estimate the relative probability of selecting a given step compared to another [START_REF] Manly | Resource selection by animals: statistical analysis and design for field studies[END_REF][START_REF] Schmeller | Animal Movement Tools (amt): R-Package for Managing Tracking Data and Conducting Habitat Selection Analyses[END_REF].

However, conditional regression models that include a random effect on individuals are challenging to fit [START_REF] Craiu | Conditional Logistic Regression With Longitudinal Follow-up and Individual-Level Random Coefficients : A Stable and Efficient Two-Step Estimation Method[END_REF]. As conditional logistic regression models are likelihood-equivalent to a Poisson model with stratum-specific fixed intercepts, [START_REF] Muff | Accounting for individual-specific variation in habitat-selection studies: Efficient estimation of mixed-effects models using Bayesian or frequentist computation[END_REF] proposed a new frequentist approach to fit iSSF using the glmmTMB package [START_REF] Brooks | GlmmTMB Balances Speed and Flexibility Among Packages for Zero-inflated Generalized Linear Mixed Modeling[END_REF]. glmmTMB provides faster results

than other packages commonly used for fitting mixed-effects SSF like coxme [START_REF] Therneau | coxme: Mixed effects cox models[END_REF] or mclogit [START_REF] Elff | mclogit: Mixed conditional logit models[END_REF]) [START_REF] Muff | Accounting for individual-specific variation in habitat-selection studies: Efficient estimation of mixed-effects models using Bayesian or frequentist computation[END_REF].

We performed the analysis using the amt R package (Signer, [START_REF] Schmeller | Animal Movement Tools (amt): R-Package for Managing Tracking Data and Conducting Habitat Selection Analyses[END_REF]. We first converted our tracking data from points to steps, considering two consecutive locations of an individual as a step. We resampled with a sampling rate of 4 h with a tolerance of 1 h to remove the irregular fixes.

Each step was defined by a geo-referenced start point, a geo-referenced end point and a start date. For each step, we extracted the land use class at the start, the land use class at the end, the air temperature and the slope of the step using the step length and the elevation difference (Fig. 1A.). We used rainfall as a categorical variable (rain / no rain) and temperature as a quantitative variable in degrees Celsius. Using conditional logistic regression, we compared these covariates with those of 200 randomly generated steps for each step (Fig. 1B), as well as their effect on step length. We define 'habitat selection' as whether animals preferentially choose (or remain in) one land use class over others [START_REF] Avgar | Integrated step selection analysis: bridging the gap between resource selection and animal movement[END_REF][START_REF] Fieberg | A 'How to' guide for interpreting parameters in habitat-selection analyses[END_REF]. We define 'habitat avoidance' as an animal tending to move at high speed, i.e. long step length in a land use class it is located in, following [START_REF] Aiello | Movement models and simulation reveal highway impacts and mitigation opportunities for a metapopulation-distributed species[END_REF]. To account for homing behaviour, we introduced a 'homing' variable, i.e. the square distance from the capture location, expressed as (x -x_capture)^2 + (y -y_capture)^2, where x_capture and y_capture are the coordinates of the capture location, and x and y the coordinates of the location under consideration. We included random effects of individuals to account for multiple observations on the same individual using the package glmmTMB [START_REF] Brooks | GlmmTMB Balances Speed and Flexibility Among Packages for Zero-inflated Generalized Linear Mixed Modeling[END_REF].

We started the analysis with a full model including all 8 covariates (effect of sex on step length, habitat selection, habitat avoidance, slope, effect of slope on step length, effect of rainfall on step length, effect of air temperature on step length and homing). We performed model selection by removing covariates one by one on the basis of the best Akaike's Information Criterion (AIC) gain and keeping the variables whose effect was significant on the basis of 95% confidence intervals. If a variable showed a significant interaction effect (e.g. step length x slope), we kept the base variable in the model in addition to the interaction following [START_REF] Brooks | GlmmTMB Balances Speed and Flexibility Among Packages for Zero-inflated Generalized Linear Mixed Modeling[END_REF]. We treated the homing variable differently, keeping it in the first models as part of the experimental design. We tested the effect of removing it at the end of the selection process, though, for illustrative purposes. Following [START_REF] Burnham | Multimodel Inference: Understanding AIC and BIC in Model Selection[END_REF] and [START_REF] Mazerolle | Improving data analysis in herpetology: using Akaike's Information Criterion (AIC) to assess the strength of biological hypotheses[END_REF], we considered the model with the lowest AIC as the best supporting model. Finally, for easier interpretation we also calculated the Akaike weights to represent the relative likelihood of each model.

Males moved significantly greater distances between steps than females (mean step length: 7.5 m versus 3.8 m, Wilcoxon test with P < 1e-9).

The best performing model including homing (as part of the experimental design) is the model including habitat avoidance, habitat selection, slope and the interaction of step length and slope (model 'no sex, no weather', Table 1).The effects of sex, air temperature and rain were not included. The homing effect was also not significant and did not appear in the best model ('No sex, no weather, no homing', Table 1). Three models had an Akaike weight >0.10. The model estimates and confidence intervals were very similar from one model to another, making interpretation easier.

Slope

A significantly negative regression coefficient (-0.152 [-0.274, -0.031] in the best performing model) for the interaction of slope and step length ('slope x step length' covariate) was included in all models (Table 1). This means that in our experiment the frogs moved more slowly in the steep areas than in the low slope areas. Note that we kept the 'slope' covariate as a main effect in all models that included the 'slope x step length' interaction, as it is recommended to keep all covariates as main effects that are included as interactions [START_REF] Brooks | GlmmTMB Balances Speed and Flexibility Among Packages for Zero-inflated Generalized Linear Mixed Modeling[END_REF].

Habitat selection

The regression coefficient for each habitat represents selection relative to grassland (which is considered the default habitat). In each model, watercourses were more attractive than any other land cover (Table 1). The effects of wetlands and ski runs were not significant, and roads did not appear in the models due to lack of data (we did not have registered locations on roads).

Habitat avoidance

Habitat avoidance was included in each model (Table 1). Ski runs were significantly (estimate = 0.686 [0.168, 1.204] in the best performing model) more avoided than grassland (i.e. frogs located on ski runs tended to move faster). Wetlands and watercourses did not differ from grassland in terms of frog avoidance.

To our knowledge, no such study using high-resolution tracking at fixed time intervals has been conducted on frogs yet. Nevertheless, the study of amphibian movements at small temporal and spatial scales could be valuable for better understanding their behaviour and scaling from the individual to the population scale [START_REF] Pittman | Movement ecology of amphibians: A missing component for understanding population declines[END_REF]. A possible reason for the lack of such studies may be the relatively large weight of GPS tags compared to the average weight of an amphibian [START_REF] Thomas | Wildlife tracking technology options and cost considerations[END_REF]. Only recently has the miniaturization of GPS technology reached a point where it is available for amphibian studies.

Our results confirmed some preferences in the way Common frogs move through different land covers. For example, we have demonstrated that the frogs tend to be attracted to watercourses in summer. This is in line with studies showing a preference for aquatic summer habitats in the mountains [START_REF] Turchin | Quantitative analysis of movements: measuring and modeling population redistribution in animals and plants[END_REF][START_REF] Cogălniceanu | Aquatic habitat use by amphibians with specific reference to Rana temporaria at high elevations (Retezat Mountains National Park, Romania)[END_REF]. The integrated step selection function allowed us to explore the effect of various covariates on movement speed as well as resource selection, providing a more complete picture than a classical resource selection model. In particular, we found that frogs were able to move faster when placed on a presumably unsuitable land use (ski runs) than when placed on a more suitable habitat such as a wetland. We interpret this as a repulsive effect of unsuitable habitats.

The choice of method for attaching transmitters to amphibians is always challenging because of the high risk of injury due to the softness of their skin [START_REF] Bull | Comparison of two radio transmitter attachments on Columbia spotted frogs (Rana luteiventris)[END_REF][START_REF] Muths | A Radio Transmitter BeJt for Small Ranid Frogs[END_REF][START_REF] Groff | Evaluation of a waistband for attaching external radiotransmitters to anurans: Attaching Radiotransmitters to Anurans[END_REF]. With the type of harness we chose based on the literature, we experienced a 100% injury rate (in particular, we observed traces of skin lacerations), which is much higher than that obtained with lighter radio transmitters [START_REF] Groff | Evaluation of a waistband for attaching external radiotransmitters to anurans: Attaching Radiotransmitters to Anurans[END_REF]. Therfore, while the use of GPS transmitters for frog movement studies is promising, improved techniques for attaching external transmitters to animals are needed to prevent animal injury. Further research is needed to improve the attachment system, for example by testing harnesses higher on the body, until even lighter GPS tags become available.

The behaviour of the Common frog changes considerably during the year [START_REF] Miaud | Variations in life-history traits in the common frog Rana temporaria (Amphibia: Anura): a literature review and new data from the French Alps[END_REF]. This study was only conducted during the summer when adults are mainly foraging and resting. The sedentary nature of the species in summer, coupled with the short battery life, led us to relocate the frogs for the purposes of the experiment. As a result, the observed movements and space use may differ from natural movements of the species at this time of year. Summer movements represent only a small part of the frogs' movements: they also move during juvenile dispersal and adult migrations [START_REF] Pittman | Movement ecology of amphibians: A missing component for understanding population declines[END_REF]. A promising extension of this work would be to replicate it during one of these phases.

They are relatively short, and a battery life of just a few days or weeks might be sufficient to study these events.

Our study contributes to the knowledge of the movements of the Common frog through different land cover at very fine temporal and spatial scales. Technological advances will provide new opportunities in the future to track smaller animals for longer periods of time. This will allow us to better understand the movement of small animals across the landscape and the impact of human infrastructure on these movements. Our results are relevant from a conservation perspective in human-transformed mountain landscapes.

Figure and table legends

Figure1.

  Figure1. Frog movement modelling. Considering a constant time interval (4 hours), a step was defined by a start point, an end point and a start date T. For each step, we

Table 1 .

 1 Results of the models analysed. For each covariate, the coefficient estimate, standard error and 95 % confidence intervals (95 % CI). The differences in AIC with the best performing model are shown as ΔAIC, i.e. as the Akaike weight. Significant results

	at	95%	are	shown	in	bold.

Acknowledgements

This study was funded by the Agence de l'eau Rhône-Méditerranée-Corse (French water agency). The authors would also like to thank Claude Miaud for his valuable advice and the Les Arcs ski resort for its support and data.

The captures and, more generally, the entire experiment were carried out in compliance with the French laws on protected species. The Prefecture (administrative centre) of the Savoie department authorized the experiment in May 2017.

Data availability

The tracking data are available via MoveBank ("Common frog -Rana temporaria -Les Arcs, Savoie, France", ID 2630735956, managed by EB).