Siyi Zhou

Fellow, IEEE Anthony Grbic
email: agrbic@umich.edu

An 8×4 Continuous Transverse Stub Array fed by Coaxial Ports

Keywords: Continuous transverse stub, slot arrays, wide band antennas

Continuous transverse stub arrays are wide band, wide scanning antennas consisting of an arrangement of long slots or parallel plate waveguide apertures radiating in free space. A line source is generally required to feed these arrays. Here, we show that such a line source can be created over the radiating aperture using a 2D arrangement of coaxial probe transitions. The coaxial transitions are directly integrated into the parallel plate waveguides feeding the slots. Such a solution avoids using quasi-optical systems or bulky corporate networks to feed the array. The proposed 2D feeding scheme also allows steering the main beam of the array. This is an additional benefit with respect to previous designs for which scanning was limited to a single plane. An array of 8×4 elements validates the concept at 5.8 GHz. Measurements show that the array exhibits a field of view of ±30 • in elevation over the 5.4 -6.2 GHz band, with an active reflection coefficient for the central elements better than -10 dB.

I. INTRODUCTION

T HE continuous transverse stub (CTS) array is an established solution for wide band and wide scanning Satcom antenna applications [START_REF] Milroy | Continuous transverse stub element devices and methods of making same[END_REF]- [START_REF] Ettorre | Continuous transverse stub array for Ka-band applications[END_REF]. The basic radiating element is a non-resonant, long slot or broad stub fed by a parallel plate waveguide (PPW) network. An array of such elements can be fed either in series or in parallel. Both feeding architectures require a line source to properly illuminate the array. The line source can be realized using a quasioptical system [START_REF] Ettorre | Continuous transverse stub array for Ka-band applications[END_REF] or by integrating active components within the PPW feeding network [START_REF] Robertson | Transverse device array radiator ESA[END_REF], [START_REF] Lee | MMW electronically scanned antenna[END_REF]. Generally, quasi-optical systems are used in combination with a corporate feed system. Such a solution preserves the large bandwidth behaviour of CTS arrays, but limits the scanning ability of the array to a plane parallel to the radiating slots [START_REF] Ettorre | Continuous transverse stub array for Ka-band applications[END_REF].

Here, we use coaxial probe transitions to feed a CTS array. The coaxial transitions are directly integrated into the PPW lines feeding each radiating slot to generate the required line source. In this way, each slot is fed in parallel, as in a corporate network while preserving the compactness of the structure. The proposed feeding system also offers the possibility to steer the main beam of the array in any direction in free space once the required phase and amplitude excitations are provided at the input ports of the coaxial probes.

The design of an array of four slots, each fed by eight coaxial probes (8×4 input ports), is proposed to validate the concept at an operating frequency of 5.8 GHz. The active reflection coefficient of the array's unit cell is evaluated in an infinite array environment for scanning over the principal planes of the array. Each unit cell of the array is fed by a coaxial transition, which allows scanning range ±30 • in elevation from 4.8 GHz to 6.2 GHz. This corresponds to a fractional bandwidth of 24% around 5.8 GHz. A prototype of the array is manufactured from aluminum using a standard milling process. The measured active reflection coefficient of the central elements of the finite array is compared to full-wave simulations, and to the infinite case validating the design and general conclusions. Measured radiation patterns are also validated through full-wave simulations. Measurements demonstrate that the antenna can steer its main beam in the both principal, and diagonal planes over a field of view of ±30 • , while maintaining cross-polarization levels below over -20 dB.

The paper is organized as follows. Section II presents the design of the unit cell of the array fed by coaxial transitions. The active reflection coefficient of the unit cell is provided for scanning angles up to 30 • . The prototype and the measured active reflection coefficient and radiation patterns are discussed in Section III. Finally conclusions are drawn in Section IV.

II. ANTENNA DESIGN

The architecture of the 8×4 CTS array fed by coaxial probes is shown in Fig. 1a. Each of the four slots comprising the array is fed by eight coaxial ports through air-filled PPW lines. The unit cell of the array, with a coaxial probe transition, is highlighted in Fig. 1a. Side views of the unit cell in the xzand yz-planes are also provided in Fig. 1b. The design of the radiating slots of the array follows the procedure outlined in [START_REF] Foglia Manzillo | Active impedance of infinite parallel-fed continuous transverse stub arrays[END_REF]. The slot width, ws, and height of the feeding PPW lines are chosen to only allow the propagation of the Transverse Electromagnetic (TEM) mode of the PPW lines at the arrays's upper frequency of operation. The slot width ws and periodicity dy are designed to yield an active reflection coefficient over the slot plane (reference plane R1 in Fig. 1b) lower than -10 dB for the operating band and scanning range. A two step quarter-wave impedance transformer is then used to match the active impedance of the slot to the input PPW line (reference plane R2 in Fig. 1b) where the coaxial probe transition is located. The input PPW line is then matched to the 50 Ohm impedance of the coaxial transition using a back short and a cylindrical intrusion within the PPW [START_REF] Pozar | Microwave engineering[END_REF] (refer to Fig. 1b for geometrical details). In particular, the cylindrical intrusion within the PPW and a rectangular cavity around the connection of the probe transition (refer to Fig. 1b) are employed to match over the band of interest. Full-wave simulations in an infinite array environment are used to derive the final geometrical dimensions of the unit cell as provided in Fig. 1. The periodicity along the x-axis (dx) of the coaxial input ports is set to less than a half wavelength at the upper frequency of operation to avoid grating lobes. Specifically dx is chosen equal to dy = 24 mm. Note that the antenna is linearly polarized with the electric field of the feeding TEM mode oriented along the y-axis. The E-and H-plane correspond to the yz-plane and xz-plane in Fig. 1. The bandwidth, frequency of operation and scanning range specification for the design are chosen based on possibly using the array as a Van Atta mirror in a far-field wireless power transfer system [START_REF] Ettorre | Radiative wireless power transfer system using wideband, wideangle slot arrays[END_REF], [START_REF] Ettorre | 2D Van Atta array of wideband, wideangle slots for radiative wireless power transfer systems[END_REF]. In particular, the goal was an active reflection coefficient lower than -10 dB over the 5.4 -6.2 GHz band, for a scanning range in elevation of ±30 • .

Fig. 2a provides the active reflection coefficient of the unit cell from 4.8 to 6.2 GHz at the reference planes R1, R2 and at the SMA connection for broadside direction. The wide band behaviour of the radiating slot at the reference plane R1 is highlighted by a flat active reflection coefficient in the entire band. As expected, the two step-quarter-wave transformers introduces a resonance at the design frequency of 5.8 GHz, but does not affect the wide band behaviour of the unit cell. The same behaviour is observed at the SMA connection after the coaxial probe transition. In addition, Fig. 2b plots the active reflection coefficient of the unit cell from 4.8 to 6.2 GHz along the E-, D-(diagonal plane, φ = 45 • in Fig. 1) and H-plane at broadside θ = 0 • and θ = 30 • . The unit cell is matched over the considered band (24% relative bandwidth around 5.8 GHz) and scanning range. Note that the coaxial transition allows 2D scanning (refer to Section III) and does not require a corporate feed network or quasi-optical system, as in [START_REF] Ettorre | Continuous transverse stub array for Ka-band applications[END_REF]. It is worth mentioning that connected arrays can provide a similar performance [START_REF] Cavallo | Connected-slot array with artificial dielectrics: a 6 to 15 GHz dual-pol wide-scan prototype[END_REF]- [START_REF] Yetisir | Ultrawideband array with 70 • scanning using FSS superstrate[END_REF].

III. PROTOTYPE AND MEASUREMENTS

The array prototype is shown in Fig. 3. It is made of various aluminium parts fabricated using a computer numerical control (CNC) milling machine, and assembled as outlined in [START_REF] Ettorre | Continuous transverse stub array for Ka-band applications[END_REF]. The assembly uses dowel pins and screws with an expected alignment accuracy better than 50µm. The 32 SMA connectors used for the input ports of the array are visible in Fig. 3a. During measurements, coaxial cables were attached to the SMA connectors to ease access to the input ports of the array. The cables were not considered in the full-wave simulations of the array.

The scattering matrix (32×32 elements) of the array was measured. The active reflection coefficient at each input port of the array was then derived by assuming a uniform illumination and the required phase profile for scanning [START_REF] Pozar | The active element pattern[END_REF]. The active reflection coefficient for the central element of the array (Port 12 in Fig. 3b) is shown in Fig. 4a for a broadside excitation. Full-wave simulations of the finite and infinite array are also reported for comparison. The measured active reflection coefficient is in line with the infinite and finite array numerical results. Please note that de-embedding was performed on the measured results to remove the impact of the cables on the active reflection coefficients. The measured active reflection coefficient for the central element for scanning at θ = 30 • in elevation is reported in Fig. 4b along the E-, D-and H-planes. The simulated active reflection coefficient for the central element of the array is provided for comparison in the considered scanning directions. The central element is matched over the design band 5.4 -6.2 GHz and even beyond. It is worth mentioning that similar results were achieved for all other input ports, except for the most external ones as Port1 (see Fig. 3b). This is expected for such a small array. Different aperture illuminations may be used to improve the matching of the external elements of the array.

The 3D embedded element patterns corresponding to each input port of the array were measured in the anechoic chamber at IETR by feeding the considered port and terminating all other ports with The measured radiation patterns along the E-, H-and D-planes at 5.8 GHz are shown Fig. 6 for two different scan angles. The radiation patterns have been normalized to their maximum. The 2D scanning ability of the array is validated for the CTS array. The 2D scanning ability is enabled by the proposed coaxial probe transition and antenna architecture. The proposed array also exhibits low crosspolarization levels (< -20 dB) in all planes and for all the considered scanning angles [START_REF] Ludwig | The definition of cross polarization[END_REF]. These results confirm the polarization purity of the radiated field. Similar measured results, in terms of scanning, are obtained in the band 5.4 -6.2 GHz and not reported here for brevity.

The measured realized gain and directivity of the array for a uniform illumination are estimated equal to 18.6 dBi and 17.8 dB, respectively, at broadside at 5.8 GHz. The total loss of the antenna is equal to 0.8 dB. This includes the metallic, cable and transition losses. The major contribution to the losses is attributed to the cables which are 30.48 cm long with losses on the order of 0.6 dB.

IV. CONCLUSION

An 8×4 continuous transverse stub array fed by coaxial probes has been presented. Each slot of the array is fed by eight equallyspaced coaxial probes in the PPW lines feeding the slots. The proposed feeding scheme allows 2D steering of the antenna main beam in free space. Such a solution overcomes the limitations of earlier CTS designs which achieve scanning only in one plane, at a given frequency of operation. In addition, the proposed scheme does not require a quasi-optical system nor active components within the corporate feed network of the array, easing the fabrication. A prototype made of aluminum using CNC milling has been presented and validated through full-wave simulations and measurements. The active reflection coefficient of the array is less than -10 dB over the band 5.4 -6.2 GHz for scanning up to 30 • in elevation. Measurements show that the antenna can steer its main beam over the considered range with cross-polarization levels below -20 dB. The proposed antenna may be a good candidate for applications requiring a wide band, wide scanning antenna. The proposed antenna could be used as a Van Atta mirror for far field wireless power transfer applications.

  Fig. 1. The 8×4 CTS array. (a) Perspective view. The unit cell of the array is outlined by a dashed box. (b) Side view of the unit cell of the array along the yzand xz-planes. The dimensions are in mm.

Fig. 2 .

 2 Fig. 2. Active reflection coefficient of a unit cell of the array in an infinite periodic environment. (a) At the reference planes R1 and R2 in Fig. 1 for broadside radiation. (b) At the SMA connection for different scanning angles and planes of observation.

Fig. 3 .

 3 Fig. 3. Prototype. (a) Perspective view. (b) Rear view showing the labelled input ports. The coaxial cables and mechanical support used for measurement are visible in the photograph.

Fig. 4 .

 4 Fig. 4. Active reflection coefficient of the central element of the array (P12 in Fig. 3b). (a) Broadside radiation. (b) Scanning in E-, D-and H-plane at θ = 30 • . The active reflection coefficient of the unit cell for broadside radiation in an infinite array environment is shown for comparison.

Fig. 5 .

 5 Fig. 5. Normalized radiation patterns of the array for a uniform illumination along the E and H-plane for broadside radiation at 5.8 GHz.

Fig. 6 .

 6 Fig. 6. Normalized radiation patterns of the array for a uniform illumination and different scan angles at 5.8 GHz. (a) E-plane. (b) H-plane. (b) D-plane.

  A c c e p t e d M a n u s c r i p t

Manuscript received XX/This work was supported in part by the French National Research Agency (ANR) under grant n • ANR-14-CE26-0030-01, the UM-KACST Joint Center for Microwave Sensor Technology, the European Union through the European Regional Development Fund (ERDF), and the French region of Brittany, Ministry of Higher Education and Research, Rennes Métropole and Conseil Départemental 35, through the CPER Project SOPHIE / STIC & Ondes. S. Zhou and M. Ettorre are with the Institut d'Electronique et de


Anne-Gwénaëlle Guezennec
email: a.guezennec@brgm.fr

Agathe Hubau

Jérôme Jacob

Simon Chapron

Chris Bryan

Catherine Joulian

Title. Bioleaching of a polymetallic residue: influence of the temperature on the sulfide leaching yield

Keywords: bioleaching, nickel, copper, cobalt, pyrrhotite, pentlandite, chalcopyrite, temperature, mining residues

The mining of non-ferrous metals produces the largest volume of metal-containing, extractive waste in Europe, and about 29% of all the waste produced in the EU-28. In the frame of the European project NEMO (Near-zero-waste recycling of low-grade sulfidic mining waste for critical-metal, mineral and construction raw-material production in a circular economy), new ways to valorise sulfidic tailings are being developed through the recovery of valuable metals and critical raw materials and the transformation of the residual in clean mineral fraction to be used for the mass production of cement, concrete and construction products. The first step of NEMO concept consists in removing the sulfides remaining in the tailings and extracting the residual metals using either enhanced bioleaching or alkaline autoclave conversion processes. This paper focuses on one of the project case study, the residues obtained at an operating heap leaching plant (Terrafame, Finland). This material still contains several sulfidic minerals (pyrrhotite, pyrite, sphalerite, pentlandite, violarite, chalcopyrite) and significant amounts of metals (Zn, Ni, Cu, Co, REEs). The study aimed at increasing metals leaching yield. Bioleaching tests were performed first in shake-flasks and then in stirred tank reactors (2L) at increasing solid concentration (from 3 to 10%) and at three temperatures using three microbial cultures growing at 42°C, 48°C, 55°C.

The results show that Ni is released very quickly suggesting that part of Ni dissolved in the primary heap is re-precipitated and remains in the residues. In the contrary, Cu dissolution is much slower but the kinetics is substantially improved when the temperature is increased

Introduction

In Europe, most of the primary resources with high or moderate metal grade, reasonable accessibility and easy to process are exhausted. In today's context of resource scarcity, complex low grade ores and metal-containing, extractive waste get more and more attention. As existing processes and technologies are often not profitable for these types of unconventional resources, alternative routes still need to be developed to address the complexity of composition while remaining cost effective.

In this context, bio-hydrometallurgy appears more and more as an ecologically acceptable and yet economic alternative for the recovery of metals in low-grade sulfidic materials. However, sustainable development of biomining methods cannot target only the extraction of metals but should also include an effective strategy to valorize the non-metallic fractions and thus to reduce drastically the generation of "ultimate" wastes. The European research project NEMO (Near-zero-waste recycling of low-grade sulfidic mining waste for critical-metal, mineral and construction raw-material production in a circular economy) aims at valorizing sulfidic tailings by combining innovative hydrometallurgical processes (including bioleaching) for the recovery of valuable metals and critical raw materials and the transformation of the residual in clean mineral fraction to be used for the mass production of cement, concrete and construction products. This paper deals with the development of enhanced bioleaching methods initiated in the framework of NEMO and aiming at recovering metals remaining in the residues obtained at an operating heap leaching plant (Finland). It focuses on the comparison of three microbial cultures with different optimal temperature (42°C, 48°C, 55°C) and their influence on the leaching kinetics and the metal yields.

Materials and methods

Three microbial consortia selected from BRGM culture collection were used: BRGM-KCC (optimal temperature: 42°C), dominated by Leptospirillum (L.) ferriphilum, Acidithiobacillus (At.) caldus and Sulfobacillus (Sb.) spp., Tw48 (optimal temperature: 48°C) and N55 (optimal temperature: 55°C), both dominated by At. caldus and Sb. thermosulfidooxidans. The cultures were grown in a nutrient medium called "0Km" optimised for bacterial growth on sulfidic materials. Its standard composition is the following: (NH4)2SO4, 3.70 g L -1 ; H3PO4, 0.80 g L -1 ; MgSO4•7H2O, 0.52 g L -1 ; KOH, 0.48 g L -1 .

The microbial consortia were first grown in shake flasks with a solid concentration of 3%. After several sub-culturing, the biological activity and the biomass reached a steady-state and the cultures obtained in shake flasks were used to inoculate 2L stirred tank bioreactors. The agitation was p erformed using a dual impeller system (axial/radial) consisting of a standard 6-blade Rushton turbine in combination with a 3-blade 45° axial flow impeller. Air enriched with CO2 (1% v/v) was injected beneath the turbine at the bottom of the reactor via a stainless steel pipe at a constant gas flow rate (120L/h). The gas flow rate was chosen in order to avoid any oxygen or carbon limitations in the system. The bioreactors were operated in batch mode and two solid concentrations were tested: 5 and 10% (w/v). The bioreactors were jacketed for warm water circulation in order to maintain a constant temperature in the pulp. The pH was maintained below 1.8 by adding concentrated sulfuric acid when needed. Fe, Cu, Ni, Co and Zn concentrations in the leachate were determined daily by atomic absorption spectroscopy using a Varian SpectrAA-300. Species-specific microbial community composition and abundance were also monitored using quantitative real-time PCR (qPCR).

Results

The increase of the redox potential, which denotes the microbial activity of Fe-oxidising microorganisms, was faster in the bioreactors inoculated with BRGM-KCC compared to the ones inoculated with Tw48 and N55 (Fig. 1). This might be explained by the presence of L. ferriphilum in BRGM-KCC consortium. This bacterium is known to oxidise Fe more quickly than other Fe-oxidising microorganisms.

Discussion

Terrafame ore is mainly dominated by pyrrhotite and pyrite whereas the nickel and zinc minerals of interest, pentlandite and sphalerite, are minor constituents of the ore. In a recent study, Arpalahti & Lundström show that Ni, Zn, Co and Cu released in the solution are partially precipitated in the current Terrafame heap operation. They suggest that these metals can react directly with pyrrhotite due to the low redox conditions encountered in the heap through a phenomenon called metathesis according to the following equation:

𝐹𝑒 7 𝑆 8 + 𝑀𝑒 2+ = 𝐹𝑒 6 𝑀𝑒𝑆 8 + 𝐹𝑒 2+
The newly formed-minerals can be leached quickly when the redox potential increases. The presence of these secondary metal sulfides in the residues might explain the quick release of metals at the beginning of the bioleaching tests of the present study. The metals dissolution kinetics (Fig. 2) suggest that most of the Ni remaining in Terrafame residue is contained in this kind of minerals since Ni is released very quickly in the solution at the beginning of the tests. In contrary to Ni, only a few part of remaining Zn, Cu and Co is released at the beginning of the bioleaching tests; the dissolution kinetics follow then a more conventional leaching curve. It is likely that the Zn, Cu and Co-bearing minerals (sphalerite, chalcopyrite and pyrite) originally present in the ore are not completely leached in the heap and remain in the residue. When subjected to oxidative leaching conditions, these minerals are leached following the order of nobility of sulfides as can be seen in Fig. 2: sphalerite first, and then chalcopyrite and pyrite. The limited dissolution yield of Cu is probably linked to the recalcitrant nature of chalcopyrite and to the massive Fe precipitation observed during the leaching tests. This phenomenon has been extensively reviewed and the dissolution limitation of chalcopyrite can be partially overcome by increasing the temperature as confirmed by the leaching yields obtained with the three consortia, BRGM-KCC, Tw48 and N55.

Conclusion

The bioleaching tests performed in aerated stirred-tank bioreactors in the frame of NEMO project enabled to understand better the leaching behavior of a complex sulfidic residue. The results show that a substantial portion of Ni, Zn and Co remaining in these residues can be recovered using this method while the sulfide content is reduced drastically. The next steps of the study will consist in (i) testing new operating conditions to improve chalcopyrite leaching and (ii) studying the use of the sulfide-free residues for the production of cement, concrete and construction products. The environmental and economic sustainability of the developed processes will be further assessed.

Fig. 1 :

 1 Fig.1: Redox potential and Fe leaching yield over the time at 42°C (KCC), 48°C (Tw48), 55°C (N55). The redox increase was followed by the dissolution of Fe in the first days of the tests. When dissolved Fe concentration reached 2000 mg/L, which corresponds approximately to Fe yield of 20%, it remained constant then over the time in the case of the bioreactor inoculated with BRGM-KCC consortium and maintained at 42°C. In the case of Tw48 and N55 consortia, Fe dissolved concentration decreased. This phenomenon is probably linked to the precipitation of FeIII under the form of jarosite. As can be seen in Fig. 2, Ni leaching kinetics was very fast and Ni yield reached almost 80% after less than 2 days. Zn leaching yield reached 80% after 8 days. While 40 % of Co was leached

Fig. 2 :

 2 Fig. 2: Zn, Ni, Co and Cu leaching yield over the time at 42°C (KCC), 48°C (Tw48), 55°C (N55).

Acknowledgement: This work has received funding from the European Union's Horizon2020 research and innovation program under grant agreement No 776846. The authors thank Terrafame company for the samples provision.


Victoria Rapos

PhD Michael E Cinelli
email: mcinelli@wlu.ca

Natalie Snyder

Armel Crétual

Anne-Hélène Olivier

RUNNING HEADER: MPD WITH CHILDREN AND ADULTS Minimum Predicted Distance: applying a common metric to collision avoidance strategies between children and adult walkers

Tested collision avoidance strategies between middle-aged children and adults • Minimum Predicted Distance (MPD) is a metric describing risk of collision over time

• MPD can be used to predict future collisions in middle-aged children • MPD is consistently lower when a child is involved compared to adults • Regardless of age the walker passing second contributes more to MPD than walker one

Vision is the primary sensory system to provide rich environmental information at a distance to determine appropriate collision avoidance strategies with obstacles [START_REF] Croft | Watch where you're going? Interferer Velocity and visual behavior predicts avoidance strategy during pedestrian encounters[END_REF][START_REF] Patla | Understanding the roles of vision in the control of human locomotion[END_REF]. Visual information in the form of optic flow informs observers about their rate and direction of movement within an environment as well as the movement of an environment relative to them [START_REF] Gibson | The senses considered as perceptual systems[END_REF]. In addition, retinal expansion of an object can be used to estimate an individual's timeto-collision (TTC) with an obstacle by detecting velocities and angles [START_REF] Cinelli | Travel path conditions dictate the manner in which individuals avoid collisions[END_REF]. TTC can be predicted between two walkers up to 10 seconds prior to contact based on gaze angles, becoming more accurate as contact time decreases [START_REF] Cutting | How do we avoid collisions with stationary and moving obstacles[END_REF][START_REF] Savelsbergh | Grasping tau[END_REF]. Visual information is then used to alter one's locomotor behaviour to successfully avoid an approaching obstacle. When considering collision avoidance between two walkers, TTC does not consider the mutual adaption required between the two walkers to successfully avoid one another.

A C C E P T E D M A N U S C R I P T

Collision avoidance strategy between two adult walkers is the result of mutually controlling their Minimal Predicted Distance (MPD) [START_REF] Olivier | Minimal predicted distance: A common metric for collision avoidance during pairwise interactions between walkers[END_REF]. MPD accurately predicts the distance at which two walkers would collide if their speed and path trajectory were maintained at first sight of one another [START_REF] Olivier | Minimal predicted distance: A common metric for collision avoidance during pairwise interactions between walkers[END_REF][START_REF] Olivier | Collision avoidance between two-walkers: Role-dependent strategies[END_REF][START_REF] Knorr | Influence of Personand Situation-Specific Characteristics on Collision Avoidance Behaviour in Human Locomotion[END_REF]. MPD calculation can be broken down into three successive stages: 1) observation phase, first sight of one another and MPD is low (i.e., a change in speed and trajectory is required in order to avoid a collision); 2) reactive phase, both individuals adapt their speed and trajectories to avoid a collision (i.e., MPD increases to 1.0m between the centre of the two young adult walkers [START_REF] Olivier | Minimal predicted distance: A common metric for collision avoidance during pairwise interactions between walkers[END_REF]); and 3) regulation phase, the maintenance of MPD (i.e., the two walkers ensuring a collision does not occur).

Collision avoidance between two young adult walkers on a 90 degree collision course also involves role-dependent strategies. The decision of which walker crosses in front is mutually determined by the two walkers' path trajectories and velocities, which involves one walker increasing or maintaining their velocity to cross first while the other walker reduces their velocity and/or orientation to cross second [START_REF] Olivier | Collision avoidance between two-walkers: Role-dependent strategies[END_REF][START_REF] Knorr | Influence of Personand Situation-Specific Characteristics on Collision Avoidance Behaviour in Human Locomotion[END_REF]. The mutual interaction between two walkers is dependent on the visual information perceived by the two walkers allowing for successful collision avoidance behaviours [START_REF] Lynch | Effect if virtual human gaze behaviour during an orthogonal collision avoidance walking task[END_REF]. By 8-12 years old children are expected to be cognitively developed and have adult-like postural control during locomotion [START_REF] Shumway-Cook | The growth of stability: postural control from a developmental perspective[END_REF]. Obstacle avoidance behaviours in children reveals high variability and different adaptive strategies compared to young adults [START_REF] Hackney | Action strategies of individuals during aperture crossing in nonconfined space[END_REF][13] The purpose of the current study was to investigate collision avoidance strategies between adults and children and to determine whether MPD can be used to predict potential collisions in children. It was hypothesized that since children have highly variable behaviours, adults will cross second because it would allow them to see the child pass in front making it safer, reducing the risk of a collision. It was also hypothesized that MPD could predict potential collisions in children, but there would be a smaller clearance distance when on a collision course with another child and a larger clearance distance when on a collision course with an adult due to the threat of injury with someone larger.

Methods:

Participants

Eighteen children (10years±1. The study was performed in a 9mx9m space with 4 occluding walls that acted as barriers to allow participants to reach steady state locomotion prior to knowing who they were interacting with and from which direction that person was walking (Figure 1). Each experimental session consisted of three children and three adults located at the four corners of the experimental space.

3D kinematic data was recorded using the Vicon system at a sampling rate of 120 Hz. In order to track each participant's movement, they wore helmets containing 4 reflective markers to represent a rigid body unique to each participant's head.

Protocol

Participants were instructed to walk at their normal pace toward the opposite corner while avoiding another walker. One baseline walking trial was completed for each participant to determine individual walking speeds and start locations to ensure interactions between participants occurred on every trial in the center of the experimental space. Participant's walking at a slower walking speed were asked to take 1-2 steps closer from the starting position in order to increase the likelihood an interaction would occur in the center of the experimental space.

Each trial required two participants, not sharing the same diagonal, to reach their opposite corner while avoiding one another. Trials were randomized and included the following interactions: 1) 30 adult-adult (AA), 2) 63 adult-child (AC), 3) 30 child-child (CC), and 4) control trials in which only one participant walked to the opposite corner of the experimental space. Each participant interacted with individuals from the same group 20 times and interacted with the opposite group 21 times. To ensure everyone had a chance to interact with one another, six block trials consisting of 24 randomized trials each, consisting of AA, AC, CC, and individual trials, were completed for a total of 141 trials.

A C C E P T E D

M A N U S C R I P T Data Analysis
The location of the rigid body on each participant's head at each time point was used to compute MPD and the velocity of each participant. Data were smoothed using a 0.5 Hz low pass 2 nd order Butterworth filter to remove high stepping oscillations. Velocity was computed using the time derivative of the participant's location.

MPD was computed at each instant of time(t) such that MPD(t) represented the distance at which the two participants would meet if no speed or path adaptation occurred at that instant in time [START_REF] Olivier | Minimal predicted distance: A common metric for collision avoidance during pairwise interactions between walkers[END_REF]. For all analyses, trials were separated into the following four groups based on the interaction and who crossed first: 1) adult-adult (AA), 2) child-child (CC), 3) child-adult passing second (CA), and 4) adult-child passing second (AC). Trials were successfully reconstructed from the time individuals first saw one another (tsee) to the time of crossing (tcross). MPD(tsee) is the initial predicted distance of crossing at time tsee, when participants crossed the occluding walls and could first see one another, MPD(tcross) occurs at dmin, the minimum distance between the two participants at time of crossing. MPD(t) is a positive progression measured from the center of one individual to the center of the other individual. A negative MPD(tsee) means an inversion in walking order occurred such that walker #1 was intended to pass first however stopped to allow walker #2 to pass first.

Inversions of MPD(t), when tsee was negative, were subsequently removed from further analyses. To ensure an adaptation to an individual's collision avoidance strategy occurred, a threshold was determined by subdividing data at MPD(tsee) by 0.1m in ascending order and compared to MPD(tcross). Within each interaction group MPD(tsee) values were subdivided into bins of 0.1m based on ascending MPD(tsee) values (Figure 2).

A C C E P T E D M A N U S C R I P T

A temporal normalization of the interaction from tsee to tcross was conducted for each trial to enable comparisons. Temporal normalization normalizes the progression of MPD to a percent of time. Adaptations in MPD(t) by the walker passing first (participant #1) were examined relative to the participant giving way (participant #2) [START_REF] Olivier | Collision avoidance between two-walkers: Role-dependent strategies[END_REF]. Collision avoidance strategies were analyzed on the normalized reaction phase and avoidance strategies were compared between groups. Contributions to MPD(t) of each walker were revealed by computing the partial derivatives of MPD(t) relative to motion adaptations performed by participants as calculated in Olivier et al. [START_REF] Olivier | Collision avoidance between two-walkers: Role-dependent strategies[END_REF]. The partial derivative calculation allowed to determine how much adaption to MPD(t) occurred when speed or path orientation varied between the two walkers. When determining the contribution of each walker, trials were valid when there was a minimum change of 0.05m between MPD(tsee) and MPD(tcross) as anything less would be too small of a change for an individual to change their behaviour.

Statistical Analysis

General linear models were conducted to determine MPD differences and crossing order differences between groups. Any p<.05 was deemed as significant. A paired dependent samples t-test was used to determine whether an adaptation to MPD occurred. Each group's MPD was compared at tsee and tcross to define thresholds. Significant differences between tsee and tcross would infer an adaptation to an individual's speed or path trajectory occurred in order to avoid a collision. Statistical Parametric Mapping (SPM, cf ref Friston) with post-hoc analysis was conducted in order to compare the difference in the evolution of MPD between groups from tsee to tcross. To compare the contribution of collision avoidance between participants during any given trial, an independent samples t-test using SPM were completed.

Results:

A C C E P T E D M A N U S C R I P T
No collisions occurred throughout the entire experiment. There was no significant difference between adult's (1.52 m/s ± 0.14) and children's (1.53 m/s ± 0.18) walking velocities (p>.05). The mean clearance distance(dmin) for the trials when an adaptation to an individual's collision avoidance strategies were: 0.77m (±0.15m) for AA; 0.67m (±0.15m) for CA; 0.71m (±0.15m) for AC; and 0.58m (±0.14m) for CC.

Threshold determination

For the AA interactions, when MPD(tsee) was lower than 0.9m (threshold levels 0m-0.8m), MPD(tcross) values were significantly higher than MPD(tsee). When MPD(tsee) ranged from 0.9m to 1.0m, there was no significant different between MPD(tcross) and MPD(tsee) (p>.05). When MPD(tsee) was 1.1m and greater, MPD(tcross) was significantly higher than MPD (tsee) (Table 2A).

For the CC interactions, when MPD(tsee) was lower than 0.7m (threshold levels 0m-0.6m), MPD(tcross) values were significantly higher than MPD(tsee). When MPD(tsee) was 0.7m, 0.8m, and 1.0m there was no significant difference between MPD(tcross) and MPD(tsee).

When MPD(tsee) was 0.9m and 1.1m and above, MPD(tcross) was significantly lower than MPD(tsee) (Table 2B).

For the CA interactions, when MPD(tsee) was lower than 0.8m (threshold levels 0m-0.7m), MPD(tcross) values were significantly higher than MPD(tsee). When MPD(tsee) was 0.8m to 1.0m there was no significant difference between MPD(tcross) and MPD(tsee). When MPD(tsee) was 1.1m and above, MPD(tcross) was significantly lower than MPD(tsee) (Table 2C).

For the AC interactions, when MPD(tsee) was lower than 0.8m (threshold levels 0m-0.7m), MPD(tcross) values were significantly higher than MPD(tsee). When MPD(tsee) was

A C C E P T E D M

A N U S C R I P T 0.8m to 0.9m there was no significant difference between MPD(tcross) and MPD(tsee). When MPD(tsee) was higher than 1.0m, MPD(tcross) was significantly lower than MPD(tsee) (Table 2D).

Results revealed that walkers adapted their trajectories to increase MPD(t) when MPD(tsee) was lower than 0.9m for the AA trials; 0.8m for the CA and AC trials; and 0.7m for the CC trials. Only trials below each group's thresholds were analyzed and the overall mean 𝑀𝑃𝐷 ̅̅̅̅̅̅̅ (t) and its time derivative were computed.

Minimum Predicted Distance (MPD)

SPM analysis revealed a significant difference of MPD(t) between groups (Figure 3A).

Post-hoc analysis revealed a significant difference throughout the entire evolution of MPD(t) between AA and CC trials (t>2.312, p<.001); AA and CA trials (t>2.283, p=.002); CC and AC trials (t>2.344, p<.001); CC and CA trials (t>2.344, p<0.001). There were also significant differences in the regulation phase of MPD(t) (80% to 100% of the interaction) between AA and AC trials (t>2.299, p=.043) and during the reactive phase of MPD(t) (10% to 80% of the interaction) between AC and CA trials (t>2.30, p=.038) (Figure 2). When comparing MPD(tcross), there was a statistically significant difference of clearance distance between groups (F(3,1)=28.66, p<.001, n 2 =0.156 ). Post hoc analysis showed no significant difference between the clearance distance of CA (MPD(tcross)=0.67m) and AC groups (MPD(tcross)= 0.71m). All other comparisons of clearance distance were statistically different from one another (AA MPD(tcross)=0.77m, CC MPD(tcross)=0.58m).

Derivative of Minimum Predicted Distance (MPD)

SPM analysis revealed a significant difference of the derivative of MPD(t) between groups (Figure 3B). Post-hoc analysis revealed significant differences between the observation

A C C E P T E D M A N U S C R I P T
phase (0% to 10% of the interaction) and the regulation phase (80% to 100% of the interaction) between AA and CC trials (t>2.846, p<.001); AA and CA trials (t>2.837, p<.001), CC and AC trials (t>2.863, p=0.002; p<.001), CC and CA trials (t>2.863, p=0.002,p<0.001). There was also a significant difference during the regulation phase (80% to 100% of the interaction) between AC and CA trials (t=2.849, p<0.001).

Contribution to collision avoidance

When determining the contribution of each walker during the interaction (from tsee to tcross), results revealed that both walkers contributed to the increase of MPD suggesting that collision avoidance was mutually performed by both walkers. Nevertheless, contribution of walker #2 to actively avoid a collision was greater than the contribution of walker #1 regardless of the individual (Figure 4). There was no main effect of group between children and adults for walker #1 and for walker #2. There were significant differences in the contribution to increase MPD between walker #1 and walker #2 from 0%-15% of the interaction between AA (t>2.828, p=.021); CA (t>2.819, p=.017); and AC (t>2.879, p=0.036). There were also significant differences in the contribution to increase MPD between walker #1 and walker #2 from 50%-100% of the interaction between AA (t>2.828, p<.001); CA (t>2.819, p<.001); and AC (t>2.879, p<.001). The CC trials only revealed significant differences during the observation phase (0% to 10% of the interaction) to increase MPD between the two walkers (t=2.868, p=.032).

Discussion:

The objective of the current study was to investigate the collision avoidance strategies between children and adults. It was hypothesized that children would have smaller clearance distance when on a collision course with another child and would have larger clearance distance when on a collision course with an adult.

A C C E P T E D M

A N U S C R I P T MPD(t) was analyzed from MPD(tsee) to MPD(tcross). By grouping trials according to MPD(tsee) thresholds, behaviours within groups were observed to determine whether an adaptation to MPD(t) occurred. MPD(tsee) thresholds differed based on which walkers were interacting with one another. Similar to Olivier et al. [START_REF] Olivier | Minimal predicted distance: A common metric for collision avoidance during pairwise interactions between walkers[END_REF], when two adults interacted with one another (AA), MPD(tsee) threshold was 0.9m (Figure 2a). When MPD(tsee) was below 0.9m adults avoided a future collision by increasing the distance between walkers in order to reach an acceptable crossing distance at the time of crossing. However, when one walker was a child, collision avoidance strategies changed. When an adult and child interacted, regardless of crossing order, MPD(tsee) threshold was 0.8m suggesting that a mutual adaptation occurred to avoid a future collision at the time of crossing at a smaller distance. Although the overall progression of MPD(t) is similar between children and adults, person specific characteristics, such as height and body anthropometrics, may be the driving factor causing a decrease in MPD(t) when a child and adult interacted. In addition, anthropometrics may have also played a role when two children interacted with one another as the MPD(tsee) threshold was 0.7m (i.e., adaptation occurred at a smaller distance). Throughout the entire progression of MPD(t) the distance was always smaller when two children interact compared to two adults (Figure 3A), most likely due to maintaining one's area of personal space [17]. The idea of personal space, the distance an individual will maintain when circumventing an obstacle (static and dynamic), is related to an individual's shoulder width and thus their relative safety margin. Compared to adults, children are typically smaller in size and consequently they have a smaller shoulder width. A child's relative safety margin may be similar to that of an adult when on a collision course however, the absolute safety margin differs due to the size of the individuals. A smaller individual possessed a smaller When on a collision course with an approaching walker, specific details about the approaching walker is not identified by an individual until the walker is within one's central field of view [18]. Visual acuity or fine detail about the approaching walker, such as face recognition or sex differences, are only identifiable approximately 1m from one another [18]. The only thing individuals were able to recognize at the MPD(tsee) was the size of the approaching individual. Therefore, it is unlikely the differences in MPD between groups are due to sex differences or familiarity about the two walkers and more so due to the size of the individual or the stage of development.

Middle-aged children may not have a fully developed dorsal stream which is involved with information processing, resulting in a longer time required to process collision avoidance information [19][20]. Compared to young adults, children have difficulty with perception-action coupling, misjudging passable gaps [19]. A delayed response to avoid a collision may partially explain why MPD(tcross) occurs at a smaller distance when a child is involved, since they are not efficiently synchronizing motor movements with perceptual information about the environment. A delayed response results in a longer adaptation to avoid a potential collision and a smaller overall passable distance between walkers. Since MPD(t) is an absolute measure it is unknown whether an under-developed dorsal stream is causing a difference in MPD(t) or whether it's solely due to body anthropometrics. However, regardless of the overall decrease of MPD(t) when a child is involved, it seems children are able to resolve a potential collision similar to adults.

A C C E P T E D

M A N U S C R I P T
In terms of walker contribution, the walker giving way (#2) contributed more to the avoidance than the one passing first (#1), regardless of who was interacting with one another [START_REF] Olivier | Collision avoidance between two-walkers: Role-dependent strategies[END_REF]. An individual's age and size did not change the fact that walker #2 always contributes more to the avoidance of a collision compared to walker #1 during an interaction. Visual attention may play an essential role in determining crossing order of walkers. When an individual is fixated (attending) on the goal ahead rather than the approaching walker, they will cross first [START_REF] Croft | Watch where you're going? Interferer Velocity and visual behavior predicts avoidance strategy during pedestrian encounters[END_REF].

Alternatively, the individual that crosses second is aware of the approaching walker and gives way to ensure successful collision avoidance. However, gaze data was not collected and therefore we cannot confirm that visual attention determines crossing order.

In conclusion, middle-aged children appear to have developed adult-like strategies in terms of contributing to the successful avoidance of another individual when on a collision course. Middle-aged children are able to adapt to becoming an avoider during a collision course if the situation requires it, indicating proper child motor development. Therefore, collision avoidance strategies are affected by situational rather than personal characteristics (i.e., height [17]) of an approaching individual [START_REF] Knorr | Influence of Personand Situation-Specific Characteristics on Collision Avoidance Behaviour in Human Locomotion[END_REF].

  . During obstacle circumvention tasks, children alter their gait patterns just prior to reaching the obstacle whereas adults make anticipatory adjustments well in advance to the obstacle[13]. Moreover, children are highly variable with their avoidance behaviours and require a larger safety margin during obstacle avoidance tasks such as passing through apertures[14-15]. Variability in obstacle avoidance behaviours may be due to an underdeveloped neuromuscular and/or cognitive systems[16]. It appears that middle-aged children have not fully developed adult-like obstacle avoidance strategies. However, these results have focused on children's collision avoidance strategies with respect to stationary obstacles and there is a lack of research regarding collision avoidance strategies of an approaching walker. Although collision avoidance in a dynamic context happens daily, it is unknown whether middle-aged children have developed adult-like behaviour of mutually contributing to the avoidance of an approaching walker.

  shoulder width (based on anthropometrics), resulting in a smaller absolute safety margin required to pass one another when on a collision course. Therefore, the overall decrease in MPD(t) may be determined by the size of the individual.

  , L.A. & McFadyen, B.J. (2005). Children use different anticipatory control strategies than adults to circumvent an obstacle in the travel path. Experimental Brain Research. 167, 119-127. 14. Hackney, A.L. & Cinelli, M.E. (2011). Action strategies of older adults walking through apertures. Gait Posture, 33(4):733-736 15. Wilmut, K. & Barnett, A.L. (2011). Locomotor behaviour of children while navigating through apertures. Exp Brain Research, 210(2): 185-94 16. van Basten, B. J., Jansen, S. E., & Karamouzas, I. (2009). Exploiting motion capture to enhance avoidance behaviour in games. In A. Egges, R. Geraerts, & M. Overmars (Eds.), Motion in games (pp. 29-40). Berlin, Germany: Springer. 17. Gérin-Lajoie, M., Richards, C.L. Fung, J., & McFadyen, B.J. (2008). Characteristics of personal space during obstacle circumvention in physical and virtual environments. Gait and Posture, 27(2), 239-47 18. Kandle,E.R., Schwartz, J.H., Jessell, T.M., Siegelbaum, S.A., & Hudspeth, A.J. (2013) Principles of Neuroscience (5th ed.). New York: McGraw-Hill, Health Professions Division 19. Plumert, J. M., Kearney, J. K., & Cremer, J. F. (2004). Children's Perception of Gap Affordances: Bicycling Across Traffic-Filled Intersections in an Immersive Virtual Environment. Child Development, 75(4), 1243-1253 20. Plumert, J.M., Kearney, J.K., & Cremer, J.F. (2008). Children's road crossing: a window into perceptual-motor development. Association for Psychological Science, 16(5), 255-

Figure 1 :

 1 Figure 1: Experimental Setup consisting of 4 occluding walls within a 9mx9m area. Two participants stand at the corners of the area and are given a start signal to walk to the opposite corner.

Figure 2 :

 2 Figure 2: Mean values of MPD(tsee) and MPD(tcross) for each interaction grouping by 0.1m increments for: A) adult-adult (AA) interactions, B) child-child (CC) interactions, C) child-adult (CA) interactions, and D) adult-child (AC) interactions.

Figure 3 .

 3 Figure 3. A) Mean MPD(t) evolution over time without an inversion for each group and B) MPD(t) time derivative for each group without an inversion. The shaded areas represent the subject variability within in each group.

Figure 4 .

 4 Figure 4. Contribution (mean and SD) to MPD between walker #1 and walker #2 between A) adult adult interactions, B) child-adult interactions, C) adult-child interactions, and D) childchild interactions.

Table 1

 1

	5, 146.6 cm±11.7, 8 females) and eighteen adults