Michail Chalkiopoulos

Anstassios Charitopoulos
email: anastasios.charitopoulos@univ-poitiers.fr

Michel Fillon

Christos I Papadopoulos

Effects of thermal and mechanical deformations on textured thrust bearings optimally designed by a THD calculation method

Keywords: Parallel surface thrust bearings, Surface texturing, Optimisation, TEHD regime, _____________________________________________________________________________________________

A performance optimisation study of a thrust bearing with surface texturing has been addressed. Bearing response calculations have been performed with a thermohydrodynamic modelling approach. A THD-optimal bearing design has been calculated, and a sensitivity analysis has been performed. The optimal design has been evaluated utilising a thermoelastohydrodynamic model, in order to quantify the effects of thermal deformations on tribological characteristics, and a sensitivity analysis demonstrated a small difference on the parameter set of the optimal geometry. However, bearing performance is substantially affected by thermal deformations, leading to a reduction of thrust load by 13% and an increase of friction coefficient by 10%. The presented results highlight the importance of modelling thermal deformation on the design of textured thrust bearings.

INTRODUCTION

Many studies have been conducted aiming at optimising texture design and evaluating the effects of texturing on the tribological characteristics of thrust bearings [START_REF] Rahmani | Optimization of partially textured parallel thrust bearings with square-shaped micro-dimples[END_REF][START_REF] Fu | An Optimum Design Approach for Textured Thrust Bearing With Elliptical-Shape Dimples Using CFD and DOE Including Cavitation[END_REF][START_REF] Brizmer | Laser Surface Textured Parallel Thrust Bearing[END_REF]. In most of the studies, the conclusion drawn was that, for each application, the optimal texture parameters differ (in terms of texture region, shape, and depth), thus individual studies need to be performed on a per-case basis [START_REF] Gropper | Hydrodynamic lubrication of textured surfaces: A review of modeling techniques and key findings[END_REF]. Moreover, the optimised texture parameters have shown to improve the performance characteristics of the bearings in a narrow range of operating conditions, but both computational [START_REF] Papadopoulos | Computational Fluid Dynamics Thermohydrodynamic Analysis of Three-Dimensional Sector-Pad Thrust Bearings with Rectangular Dimples[END_REF] and experimental studies [START_REF] Henry | An experimental analysis of the hydrodynamic contribution of textured thrust bearings during steady-state operation: A comparison with the untextured parallel surface configuration[END_REF] have pointed out that, for high values of specific pressure, the positive effect of textures decreases dramatically, whereas, in some conditions, even a plain parallel thrust bearing exhibits better tribological characteristics than a partially textured thrust bearing optimised for different operating conditions [START_REF] Henry | An experimental analysis of the hydrodynamic contribution of textured thrust bearings during steady-state operation: A comparison with the untextured parallel surface configuration[END_REF][START_REF] Deng | Comparison of experimental, thermoelastohydrodynamic (TEHD) and thermal, non-deforming computational fluid dynamics (CFD) results for thrust bearings: part II[END_REF]. At high values of specific pressure, mechanical and/or thermal deformations of the bearing geometry become significant, therefore more advanced modelling procedures are required, in order to evaluate the optimal texture geometry of the bearings [START_REF] Hahn | The Effects of Thermal Expansion in Infinitely Wide Slider Bearings-Free Thermal Expansion[END_REF][START_REF] Dabrowski | Evaluation of water turbine hydrodynamic thrust bearing performance on the basis of thermoelastohydrodynamic calculations and operational data[END_REF][START_REF] Brockett | Thermoelastohydrodynamic Analysis of Fixed Geometry Thrust Bearings Including Runner Deformation[END_REF][START_REF] Tieu | Thermo-Elasto-Hydrodynamic-Analysis of Step and Diaphragm Thrust Bearing[END_REF][START_REF] Zhai | Numerical simulations for the fluidthermal-structural interaction lubrication in a tilting pad thrust bearing[END_REF][START_REF] Xu | A Thermal Elastohydrodynamic Lubricated Thrust Bearing Contact Model[END_REF][START_REF] Dabrowski | Evaluation of water turbine hydrodynamic thrust bearing performance on the basis of thermoelastohydrodynamic calculations and operational data[END_REF][START_REF] Zhai | Numerical simulations for the fluidthermal-structural interaction lubrication in a tilting pad thrust bearing[END_REF][START_REF] Glavatskih | The Significance of Oil Thermal Properties on the Performance of a Tilting-Pad Thrust Bearing[END_REF][START_REF] Glavatskih | TEHD Analysis of Thrust Bearings With PTFE-Faced Pads[END_REF]. The present study consists of two parts. The first part is to identify an optimal textured parallel thrust bearing geometry, for given operating conditions, utilising the state-of-the-art approach from the current literature [START_REF] Lianga | Thermo-Elasto-Hydrodynamic analysis and optimization of rubbersupported water-lubricated thrust bearings with polymer coated pads[END_REF][START_REF] Kucinschi | Thermoelastohydrodynamic (TEHD) Analysis of a Grooved Thrust Washer[END_REF][START_REF] Hartinger | CFD Modeling of a Thermal and Shear-Thinning Elastohydrodynamic Line Contact[END_REF][START_REF] Charitopoulos | Thermohydrodynamic analysis of a textured sector-pad thrust bearing: effects on mechanical deformations[END_REF]. Thus, a 3D CFD approach has been selected. A thermo-hydrodynamic (THD) model has been generated, considering viscous dissipation, solution of the energy equation in the fluid domain, and conjugate heat transfer in the solid domains. An optimisation problem has been defined, with two objective functions, namely the load carrying capacity (LCC) and the friction torque. The sector pad thrust bearing geometry modeled in the present study is a parallel thrust bearing featuring a 6 by 4 array of rectangular dimples at the inflow region of the bearing pad, in the circumferential and radial directions, respectively. The optimisation parameters of texture geometry are (a) the textured length, as a percentage of the total pad angle, (b) the textured width, as a percentage of the total pad width, and (c) the textured depth, in microns. A genetic algorithm optimisation procedure has been utilised, following the work of Papadopoulos et al. [START_REF] Papadopoulos | Geometry optimization of Textured Three-Dimensional Micro-Thrust Bearings[END_REF]. After the optimisation has been concluded, a parametric analysis has been performed in a narrow range of the optimised parameters, in order to verify that the optimised geometry is indeed the global optimum. In the second part of the present study, a thermo-elasto-hydrodynamic (TEHD) [START_REF] Jiang | Thermal Elastohydrodynamic Lubrication Analysis of Tilting Pad Thrust Bearings[END_REF][START_REF] Schenk | A Transient Thermoelastohydrodynamic Lubrication Model for the Slipper/Swashplate in Axial Piston Machines[END_REF][START_REF] Tang | A novel model for predicting thermoelastohydrodynamic lubrication characteristics of slipper pair in axial piston pump[END_REF] model has been generated, taking into consideration the mechanical and thermal deformation of the pad domain. The THD optimised geometry has been re-evaluated with the TEHD modelling approach. Moreover, a second parametric analysis has been performed, in order to identify, with the more advanced TEHD modelling approach, that the previous identified optimum is in fact the optimum while the thrust bearing operates highly loaded. Finally, the bearing performance parameters in TEHD conditions have been evaluated and compared to those corresponding to THD. The main goal of the present study is not to optimise the texture slider bearing, but in the contrary to identify why in real applications the textured configuration exhibits worst tribological characteristics, and why that the contemporary calculation methods overestimate its performance capabilities.

NUMERICAL MODEL

Basic Geometry

Three different domains make up the present computational model, namely the pad, the fluid, and the rotor, depicted in Fig. 1. The thrust bearing geometry selected for the present study, is the one presented by the experimental work of Henry et al. [START_REF] Henry | An experimental analysis of the hydrodynamic contribution of textured thrust bearings during steady-state operation: A comparison with the untextured parallel surface configuration[END_REF]. All operating conditions have been set in accordance with the aforementioned work. The dimensions of the thrust bearing can be displayed in Table 1. The gap between the rotor and the stator constitutes the lubricant domain. In order to be able to take into account the oil mixing, the groove geometry needed to be modelled. Thus, half of the fore and aft grooves have been incorporated in the geometry of the sector pad model. Including the groove geometry, helps for the more accurate representation of the hot-oil-carry-over phenomenon.

Table 1-Basic dimensions of the thrust bearing model.

Texture Geometry Parameters

The designed textured geometry consists of 24 rectangular, 6 dimples in the circumferential direction and 4 dimples in the radial direction with a texture density ρ of 80%. Schematic of the texture configuration is presented in Fig. 2. The overall textured width is calculated as a percentage of the total pad width and the textured length as a percentage of the total pad angle, excluding the grooves. The textured depth is constant for all the dimples; in the present study it is varied between 10 μm and 50 μm.

Meshing procedure

The mesh of the THD and TEHD models is identical. A detailed mesh study has been conducted, in order to evaluate the final mesh parameters. For all three domains a structured mesh has been generated, with 150 elements in the circumferential direction, and 60 in the radial. Namely the total number of elements for the three domains are: a) for the pad 910,000 elements, b) for the lubricant 340,000, with 15 layers of hexahedral elements in the cross-flow direction and 15 layers in the cross-flow direction inside the textured area, c) for the rotor 350,000 elements. The elements utilised in this study are the Solid 226 elements for the Pad geometry, and HEXA_8 for the fluid and rotor domain. In Fig. 3 a visual representation of the utilised mesh is presented. Mesh and convergence studies have been performed previously [START_REF] Charitopoulos | Numerical investigation of parallel and quasiparallel slider bearings operating underThermoElastoHydroDynamic (TEHD) regime[END_REF], and the same parameters have been utilised.

Figure 3-Mesh details

Boundary Conditions

The fluid surrounds the thrust bearing; thus, the pad is considered fully flooded. Inlet pressure of 1 bar is imposed on the fluid inner surface, as denoted in Fig. 4. Following the work in [START_REF] Papadopoulos | Computational Fluid Dynamics Thermohydrodynamic Analysis of Three-Dimensional Sector-Pad Thrust Bearings with Rectangular Dimples[END_REF], the heat transfer coefficients and temperatures have been considered accordingly, to both solid domains, see Fig. 4 and Table 2. The inner surface of the bearing pad is in contact with oil, the outer surface is in contact with air, and the bottom surface is in contact with steel (shaft), therefore, appropriate values of heat transfer coefficients have been selected at each location (more details can be found in reference [START_REF] Charitopoulos | Numerical investigation of parallel and quasiparallel slider bearings operating underThermoElastoHydroDynamic (TEHD) regime[END_REF]). The same procedure has been followed to account for the heat transfer coefficients of the rotor surfaces. The bottom surface of the pad domain has been considered fixed. The rotor domain has been considered rigid. The thermophysical properties of both solid domains' material are introduced in Table 3. The thermophysical properties of the lubricant are introduced in Table 4. The ISO VG 46 lubricant has been utilised, with a constant density of 870 kg/m 3 , and a temperature dependent viscosity. The viscosity has been modeled according to the McCoull and Walther relation [START_REF] Papadopoulos | Computational Fluid Dynamics Thermohydrodynamic Analysis of Three-Dimensional Sector-Pad Thrust Bearings with Rectangular Dimples[END_REF]:

𝑙𝑙𝑙𝑙𝑙𝑙(𝑙𝑙𝑙𝑙𝑙𝑙(𝑣𝑣 + 𝑎𝑎) ) = 𝑏𝑏 -𝑛𝑛𝑙𝑙𝑙𝑙𝑙𝑙(𝑇𝑇)
where, ν is the kinematic viscosity (cSt), T is the temperature and a = 0.6, b = 9.02865, and n = 3.52681. Finally, the rotational speed of the rotor for all the calculations of the present study has been set at 6000 RPM, the resulting sliding velocity in the mid-radius of the bearing is approximately 22 m/s.

Figure 4 -Computational model: designation of domain surfaces. Table 2 -Boundary conditions of the models. Table 3 -Thermophysical properties of the pad and rotor materials.

TEHD modelling procedure

The thermoelastohydrodynamic (TEHD) model has been generated utilising a commercial code (Ansys CFX and Ansys Mechanical). A 2-way FSI modelling approach has been utilised for the fluid/pad interface, where the CFX and FE solvers exchange data for the continuity of the temperature and pressure on both domains. In particular, (a) temperature and pressure field data are transferred from the CFD to the FE solver, and (b) mesh displacement and heat flux of the interface from the FE to the CFD solver. The bearing pad geometry can deform due to (i) the temperature gradient, and (ii) pressure generated within the thin lubricant film.

For the solution of the TEHD model, the below presented steps have been followed:

• The Finite Element solver evaluates the thermal expansion of the pad domain, for an initial temperature difference of twenty degrees Celsius. Then the transformed geometry is transferred to the CFD solver. • In the second step the flow of the lubricant domain is calculated. This includes the solution of the conjugate heat transfer in the rotor domain. • The calculated temperature and pressure profile of the fluid/pad interface are transferred to the Finite Element solver in order to re-evaluate the mesh displacement due to thermal and mechanical deformation on the pad domain. • This procedure iterates until the difference of the maximum nodal displacement of two consecutive steps is less than a preset value. • In the final step, all the tribological characteristics of the bearing are evaluated.

In order to evaluate the bearing performance on a specific minimum film thickness, five values of the initial minimum thickness of the fluid domain are selected and evaluated. The resulting minimum film thickness values are plotted versus the initial minimum film thickness, and by interpolating with a polynomial equation, the required initial minimum film thickness is evaluated. Finally, the model is recalculated in order to acquire the performance of the bearing with the wanted final minimum film thickness.

The algorithm utilised for calculating the bearing characteristics is depicted in Fig. 5. The computational time needed for the above modelling approach is approximately 5 days in a 24-core computer, for a single minimum film thickness evaluation. In comparison a simple THD model needs only 3hours on the same computer. The pad undergoes elastic deformation due to (a) pressure distribution on the fluid/pad interface, and (b) the thermal expansion of the solid. The stress is related to strain by:

{𝜎𝜎} = [𝐷𝐷] ⋅ {𝜀𝜀 𝑒𝑒𝑒𝑒 } [5]
where {𝜀𝜀 𝑒𝑒𝑒𝑒 } = {𝜀𝜀} -{𝜀𝜀 𝑡𝑡ℎ } , and {𝜀𝜀 𝑡𝑡ℎ } = [𝑎𝑎 𝑠𝑠𝑒𝑒 , 𝑎𝑎 𝑠𝑠𝑒𝑒 , 𝑎𝑎 𝑠𝑠𝑒𝑒 , 0,0,0] 𝑇𝑇 [START_REF] Henry | An experimental analysis of the hydrodynamic contribution of textured thrust bearings during steady-state operation: A comparison with the untextured parallel surface configuration[END_REF] where α se represents the coefficient of thermal expansion.

The cavitation model utilised is the Rayleigh Plesset described by the equation [START_REF] Deng | Comparison of experimental, thermoelastohydrodynamic (TEHD) and thermal, non-deforming computational fluid dynamics (CFD) results for thrust bearings: part II[END_REF].

𝑅𝑅 𝐵𝐵 𝑑𝑑 2 𝑅𝑅 𝐵𝐵 𝑑𝑑𝑡𝑡 2 + 3 2 � 𝑑𝑑𝑅𝑅 𝐵𝐵 𝑑𝑑𝑡𝑡 � 2 + 2𝜎𝜎 𝐵𝐵 𝜌𝜌𝑅𝑅 𝐵𝐵 = 𝑝𝑝 𝑣𝑣 -𝑝𝑝 𝜌𝜌 [7]
where 𝑅𝑅 𝐵𝐵 is the bubble radius, 𝛻𝛻 𝑣𝑣 is the pressure inside the bubble (the vapor pressure is calculated at the temperature of the surrounding lubricant), 𝛻𝛻 is the pressure in the liquid surrounding the bubble, 𝜌𝜌 is the liquid density, and 𝜎𝜎 𝐵𝐵 is the surface tension coefficient between the liquid and vapor. No thermal barriers are considered between the liquid and the vapor.

The calculation of the load carrying capacity (LCC) of the thrust bearing is evaluated on the fluid/rotor (FSI) interface by the following expression [START_REF] Hahn | The Effects of Thermal Expansion in Infinitely Wide Slider Bearings-Free Thermal Expansion[END_REF]:

𝐿𝐿𝐿𝐿𝐿𝐿 = ∬ 𝛻𝛻(𝑥𝑥, 𝑦𝑦) 𝑑𝑑𝑥𝑥 𝑑𝑑𝑦𝑦 𝐹𝐹𝐹𝐹𝐹𝐹 [8]
The friction torque (Fr) is evaluated on the fluid/rotor interface.

RESULTS

THD Optimisation

The THD model optimisation results are depicted in Fig 6 . The red points correspond to the Pareto optimal designs, whereas the blue points account for all the calculated intestines of the parametric model. As it can be observed from Fig. 6, no specific congestion points have been identified. The optimal design parameters that have been selected for the present study are those of the Pareto point with the smallest coefficient of friction, which is also the one with the largest value of LCC. In Table 5, the selected parameter set is presented. The resulting pressure field of the THD optimal configuration is illustrated in Fig. 7a. The maximum oil pressure has been calculated at 1.75 MPa, resulting in an overall LCC of 278.2 N, a friction torque of 0.198 Nm and a coefficient of friction of 0.0203. On the second dimple of the outer radius, a pressure drop occurs, therefore a cavitating region has been created, as seen in Fig. 7b. The maximum oil temperature has been calculated at 92.7 ℃ at the midline of the film thickness as displayed in Fig. 7d. At the fluid/pad and fluid/rotor interfaces the temperature is higher at the outer radius region of the trailing edge, as seen in Fig. 7c and Fig. 7e. The oil entering the pad is heated due to shear stresses, and the centrifugal forces force the hot oil to move at the outer radius region of the trailing edge. The temperature of the rotor is significantly higher compared to that of the stator in Fig. 7f. The calculated results are presented on Table 6.

Figure 7 -(a) Pressure field at the fluid/pad interface, (b) Volume fraction field (blue: liquid oil, red: oil vapor) at the fluid/pad interface, Temperature field at (c) fluid/pad interface, (d) midplane of Film Thickness, (e) fluid/rotor interface, (f) pad and rotor outer surfaces. Table 6 -THD Optimal Design Results

THD Sensitivity Analysis

In the vicinity of the optimal parameter set, a parametric analysis has been conducted, in order to identify the sensitivity of the design parameters. For the textured Length (L) and textured Width (B) limits of ±5% of the optimal value have been considered and for the textured Depth (TD) limits of ±3μm. As shown in Fig. 8 the local optimality is validated. Although for some parameter values the friction torque seems lower than the optimal, the LCC is also substantially decreased leading to a higher COF.

Re-evaluation of the THD-optimal design using TEHD analysis. Comparison of THD and TEHD simulation results

The optimal THD design has been re-evaluated using the TEHD based analysis. The results shown on Fig. 9a indicate a substantial alteration of the fluid/pad interface geometry due to the thermal and mechanical deformation of the pad domain. The deformed geometry affects significantly all the fields resulting in a decreased LCC and an increase of the coefficient of friction. The main evaluation results are presented on Table 7.

Table 7 -TEHD evaluation results

The mechanical and thermal deformation on the vertical axis leads to the formation of a converging region, which extends from the leading edge of the pad (inflow) to the end of the textured surface area, and a diverging region, from the end of the textured surface area to the trailing edge (outflow). The converging region results in a more efficient pressure build up in the inflow direction, due to the synergetic effect of the converging wedge and the dimple geometry. This increased pressure build-up eliminates the cavitation into the dimples, present in the THD simulations. However, because of the diverging geometry in the outflow region, the pressure drop gradient is substantially increased, therefore a cavitating region is created on the outer radius of the trailing edge as observed in Fig. 9c. The pressure-drop combined with the lower maximum pressure decreases the load carrying capacity of the bearing. The difference on the pressure and cavitation fields of THD and TEHD models is indicated on Fig. 7 and Fig. 9, while the final geometry of the lubricant film can be clearly observed in Fig. 10. Focusing on Fig. 11, we may observe that from 0° to 22.5° of the bearing, the pressure build-up of the TEHD model is slightly increased. However, from 24.5° to 45° the pressure drops sharply for the TEHD model, leading to a decreased overall pressure integral and therefore a lower value of load carrying capacity. Moreover, the overall oil temperature is lower for the TEHD model as pointed out in Fig. 12. This can be attributed to the insertion of more cold fluid into the pad domain due to the converging region in the inlet. The difference of the calculated values can be seen in table 8.

Table 8 -TEHD vs THD results comparison

To shed more light on the behavior of the pressure and temperature fields, 3D graphs of the pressure and temperature distributions at the fluid/pad interface have been generated for both the TEHD and THD models. Several pressure and temperature profiles were selected, for a wide range of radii in order to generate the 3D surface contours. In Fig. 13, it can be clearly observed that the pressure drop is steeper for the TEHD model in the outlet region. Moreover, in Fig. 13b the cavitation area for the TEHD model is highlighted. The decreased value of pressure bends the surface inwards in this region. In Fig. 14, a drop of the fluid temperature can be observed inside the dimples.

TEHD Sensitivity Analysis

A sensitivity analysis of the design parameters has been performed utilising the TEHD model. A variation of ±2% for the textured length (L) and textured width (B) has been considered and ±2μm for the textured depth (TD). The results of the THD and TEHD optima are almost identical for the textured length and depth, as seen in Fig. 13. However, for a lower value of textured width there seems to be an increase of the LCC and a decrease of the friction torque, leading to an improvement of the coefficient of friction. In Fig. 13a the pad with the decreased texture width exhibits a larger maximum pressure area, which results in an increase of LCC by approximately 1%. The temperature of the fluid is slightly higher both at the fluid/pad and fluid/rotor interfaces for this design, as seen in Fig. 16c and Fig. 16e, which results in lower viscosity in this region and therefore to a decreased value of friction torque. The overall coefficient of friction is decreased by 1%. This indicates that bearing design optimisation with THD modeling is a valuable means for identifying optimal geometric design parameters of the bearing However, for accurate prediction of bearing performance, TEHD simulations should be performed.

CONCLUSIONS

In the present work, a computational analysis of textured parallel thrust bearing has been performed. First, a thermohydrodynamic (THD) modelling approach has been used for optimising the texturing geometric parameters of the bearing, followed by a parametric analysis around the optimum, in order to validate the optimality of the obtained solution. Next, a thermoelastohydrodynamic (TEHD) modelling approach has been introduced, which takes into consideration the thermal and mechanical deformations of the pad geometry. TEHD utilises a 2-way FSI technique and has been used to re-evaluate the performance of the THD-optimal thrust bearing configuration. Finally, a sensitivity analysis of the textured geometry parameters with the TEHD model has been performed, in order to evaluate the optimality of the obtained solution with the new approach. The findings of the present study can be summarised as follows:

-The thermal deformation of the pad leads to a substantial alteration of the fluid geometry while generating a converging and a diverging region in the streamwise direction. The converging region extends from the leading edge (inflow) to the end of the textured surface area. This alteration enhances pressure build up on the inlet and hence decreases the cavitation probability within the dimples. Moreover, the converging geometry assists in increasing the inflow of cold lubricant into the pad, thus lowering considerably the overall temperature in the lubricant domain. On the other hand, the diverging region extends from the end of the textured surface area to the trailing edge (outflow). This leads to a substantial increase of the pressure drop in the outflow region, and therefore increases the cavitation probability at the outer radius of the trailing edge and decreases the load carrying capacity of the bearing. -For a given value of the minimum film thickness, the TEHD simulation results demonstrated a reduction of load carrying capacity by 13% and of friction torque by 4%, leading to an increase of the coefficient of friction by 10%, in comparison to the THD simulation results. The above results point out that bearing thermal or mechanical deformations have a substantial effect on bearing performance, therefore they should be taken into consideration in the design stage of a highperformance bearings.

Based on the present study, a direct optimisation of the texture geometry parameters by a TEHD approach is extremely expensive computationally. The most realistic approach is an optimisation of the parameters with a THD-based analysis, and the fine-tuning of the geometry details and the quantification of performance indices by detailed TEHD simulations. These are essential for bearing applications which involve high rotational speeds, high thrust loads and high lubricating oil operating temperatures.

Figure 1 -

 1 Figure 1-Calculation domains of the sector pad thrust bearing.

Figure 2 -

 2 Figure 2-Optimisation parameters of the textured geometry.

Figure 5 -

 5 Figure 5-ThermoElastoHydroDynamic analysis of parallel thrust bearings: Calculation algorithm.

Figure 6 -

 6 Figure 6 -Optimisation Pareto front.

Figure 8 -

 8 Figure 8 -THD Parametric analysis a) LCC, b) Friction torque c) Friction coefficient.

Figure 9 -Figure 10 -

 910 Figure 9 -(a) Z direction Mesh Displacement at the fluid/pad interface, (b) Pressure field at the fluid/pad interface, (c) Volume fraction field (blue: liquid oil, red: oil vapor) at the fluid/pad interface, Temperature field at: (d) the fluid/pad interface, (e) the midline of film thickness, and (f) the fluid/rotor Interface.

Figure 11 -Figure 12 -

 1112 Figure 11 -Pressure Profiles of the TEHD and THD models at a radius of 34mm.

Figure 13 - 3 -Figure 14 - 3 -

 133143 Figure 13 -3-D pressure field at Fluid/Pad interface a) THD, b) TEHD

Figure 15 -

 15 Figure 15 -TEHD Sensitivity analysis a) LCC, b) Friction torque c) Friction coefficient.

Figure 16 -

 16 Figure 16 -Pressure field at the fluid/pad interface a) -2% of optimal Textured Width, b) THD optimal, Temperature field at the fluid/pad interface c)-2% of optimal Textured Width, d) THD optimal, Temperature field at the fluid/rotor interface e)-2% of optimal Textured Width, f) THD optimal

Table 4 -Thermophysical oil properties.

 4

Table 5 -Selected Optimal Design Parameters Selected Optimal Parameter Set

 5

	Texture Length	56.20%
	Texture Width	84.70%
	Textured Depth	23 μm
	Objective Function Values
	Load Carrying Capacity	278.2 N
	Friction Torque	0.198 Nm
	Coefficient of Friction	0.0203
	Inlet Flow Rate / Pad	0.1 l/min

NOMENCLATURE H min :

Minimum film thickness (μm) V:

velocity vector (m/s) p:

the static pressure (Pa) T:

the temperature (K) τ:

the viscous stress tensor ρ:

the oil density (kg/m


Introductory note: African and Latin American migration dynamics in a comparative perspective

The idea of the conference jointly held in November 2019 at the Latin American Centre (LAC) and the Maison Traumas of Coloniality at the levels of the State, the Individual and the Nation (Ecos-Sud project C17H01 -2018-2021). Throughout 2018, Ecos-Sud researchers had been investigating and reflecting on issues of categorisation, representation and (de)politicisation of and around migrants with special reference to the displacement of representations seen through the management of bodies and the attendant use of categories involved therein. This approach led to a colloquium held at the École des Hautes Études en Sciences Sociales (EHESS) in Paris in September 2018. It was followed two months later with an international seminar on migrations and interculturality held in Santiago, Chile.

These Franco-Chilean collaborative endeavours were further enriched by serendipitous conversations and exchanges on issues of migration and borders initiated over roughly the same period with the Maison Française in Oxford, especially through the research programme on Politics, International Relations and Migration Studies headed by Prof. Thomas Lacroix, as well as the Latin American Centre run by Prof. Eduardo Posada-Carbó, and the Oxford School of Global and Area Studies. This conference therefore drew on all these exchanges and interests to jointly interrogate the variegated ways in which, following a world increase in population movement across territories and nation states in recent years migration and migrants have become an object of renewed institutional attention with resulting (un)intended effects. In particular, we were interested in how the legacies and historical traumas of coloniality may manifest themselves as the State delegates -and even subcontracts to a glut of non-governmental outfits-the procedures of symbolic and practical violence inherent to its prerogatives and yet at the same time seeks to retain control over the selection, identification, integration and/or rejection of migrants within/outside of its borders. We also aimed to investigate the various registers of cruelty towards migrants that some of these processes carry with them and asked the extent to which such cruelty is structural. Conversely, we sought to document the niches wherein all kinds of institutional actors, state, non-governmental and belonging to civil society at large may collaborate to build and provide migrants with spaces of resistance towards such violence and cruelty.

Although the main geographical focus was Latin America, research pertaining to the Mediterranean did furnish insightful comparative perspectives.

In sum, this event was aimed at promoting interdisciplinary exchange and discussion on the part of researchers involved in migration studies. Although the main geographical focus was Latin America, research pertaining to other parts of the world, especially the Mediterranean did furnish insightful comparative perspectives. Indeed, both areas have undergone similar trends in recent years. In Latin America and Africa, intra-continental migration is on the rise. According to the 2020 IOM World Migration Report, there were 21 million Africans living in another African country in 2019, against 18,5 in 2015. Similarly, the numbers of intraregional migrants in Latin America rose by 11% over the same period. And perhaps even more significantly, this rise is more important than the growth of emigration towards Northern destinations, Europe on the one hand, the US and Canada on the other. More restrictive immigration policies in the latter countries, but also better infrastructure and regional integration in new destination areas account for this shift. Furthermore, in both regions, the surge of internal movements has been brought to scholarly and media attention by the outbreak of a series of "migration crises leading to a reconfiguration of both migratory spaces. These outbreaks have been triggered by a variety of reasons: environmental crises (Ethiopia, Haiti), failing state institutions (Venezuela, Eritrea), political conflicts (Syria, Iraq, Afghanistan, Mali, Libya), economic downturn and protracted poverty (Western Africa, Central America), the conjunction of which generated mixed flows of people often forced to walk to their destinations. (1996), she was exposed to the importance of political objects in the world s greatest democracy very early on. In the following decade, she led several projects anchored in the space of school and knowledge production (LSE, Princeton, Yale) and conducted a theoretical reflection on nationalism, citizenship and secularism based on ethnographic material intersecting with the anthropology of language, body, senses and emotions (2000,2005,2008,2009), thus clearing the then new ground of emotion studies in the field of political anthropology.

Her Habilitation marked the renewal of her theoretical interests along with a geographical redeployment in Latin America where she reinvested the notion of violence as a structuring modality of historical relations, social, economic and symbolic. This has led her to conduct several projects in Colombia, especially around the anthropology of displacement , forced migration and resilience and a historical anthropology of the social memory of slavery, together with processes of forgetting and remembering. Since 2018 Véronique has been co-hosting and leading, with Chilean partners, an ECOS-SUD/CONICYT(ANID) programme on National

Con r c ion and/of O herne : Incarna ion/ Incorpora ion, Reprod c ion and Decon r c ion of Hi orical Legacie and

Traumas of Colonialism, at the levels of the State, Individuals and the Nation (2018-2021).

Furthermore, her long-standing concerns with issues of transmission have in recent years prompted her to explore aspects of co-creation and restitution in multiple forms and for various audiences. Thus, she has produced a film (2017, 2018 English, Spanish and French) as well as a poetic-political anthropology (in French [2016], translated into Spanish [2019]) and a collective volume on artistic and anthropological practices (2019).

Currently, she is working on a historio-ethnographic opera project. Finally, Véronique is also a certified practitioner of a modality of movement meditation and somatic intelligence. Since January 2016 she has introduced and developed movement-specific tools into her academic practice, whether in her seminars and workshops or in her supervision of Ph.D. students. His research interests focus on migration, identity and diasporas: the way communities perform, produce and reproduce belonging, and the spaces they create and recreate. His main areas of study cover Latin America and the Middle East, and the links between the two regions. In addition, Esteban is interested in the experiences and senses of belonging of students during and after their year abroad, including issues around identity and integration. His Ph.D. thesis research focused on the active Colombian-Lebanese community in Bogotá, focusing on their identity and the importance of social class and religion for their belonging. It followed an ethnographic approach researching the community s organisations and the divisions that social class and religion caused within it.

Claudia

Filippo Furri is a Ph.D. Candidate in Anthropology (Université de Montréal). His research focuses on Migration, Local Hospitality and the notion of Asylum/Sanctuary City . Filippo is also associated researcher in the MECMI project (Death in migration context, UQAM University/Paris Nanterre). Last but not least, Filippo is also a member of the international network Migreurop and is engaged in the Boats4people coalition, working to defend the rights of migrants at sea. Filippo is a member of the ECOS SUD Franco-Chilean programme on

Na ional Con r c ion and/of O herne (see above).

Charlotte Gregoreski is a doctoral student at the EHESS, Paris and at the Universidad de Chile, Santiago.

She has conducted work on The making of otherness and state in Chile and France compared: Immigration, race, and national construction . Charlotte is also a member of the ECOS SUD programme.

Carolina Kobelinsky: after having worked on the treatment of asylum seekers in France, based on an ethnography of waiting in asylum reception centres and a study on judgement practises at the National Court for Right of Asylum, Dr. Carolina Kobelinsky s current research concerns deaths at the borders of Europe.

She investigates the future of these "foreign deaths, often "unknown , as well as the imaginations of death of those who cross the border. Using an ethnographic approach, Carolina Kobelinksy studies the management of bodies found at the Southern borders of Europe (Spain, Italy) and explores accounts of death at the border from migrants preparing or having already succeeded in crossing the border. In doing so, the study proposes a reflection on the violence of the contemporary regime of borders and rethinks the meaning of migration as a death risk. Her research interests include Latin American immigrants in the United States and the European Union, as well as racial and ethnic inequality and discrimination in the United States, especially as it pertains to the Latin American diaspora.

Maria

  Française d Oxford (MFO) with the support of the Institut Interdisciplinaire d Anthropologie du Contemporain (IIAC) and the Laboratoire d Anthropologie des Institutions et des Organisations Sociales (LAIOS), Paris initially stemmed from an international exchange programme conducted under the aegis of ECOS French-Latin American cooperation. This 3-year programme currently headed by Prof. Benei in France and Prof. Tijoux in Chile involves a team of about six researchers on either side of the Atlantic and focuses on Migrants and National Construction: Embodiment / Incorporation, Reproduction and Deconstruction of the Legacies and Historical

  While promoting interdisciplinary exchange and discussion among researchers involved in migration studies, the papers included in the collection illustrate different aspects of these latest migratory trends. Consequently, these papers are all in varying stages of research. Filippo Furri and Yasha Maccanico (WP 20 MFO LAC 1.2) present the latest edition of the Atlas of Migrants published by the NGO Migreurop, accounting for the surge of encampment practises along migratory routes, but also of mobilisations and struggles. Likewise, Caroline Chappart (WP 20 MFO LAC 1.3) documents the formation of migrant caravans in Mexico on their way to the US, and Esteban Devis-Amaya of Venezuelans to Colombia (WP 20 MFO LAC 1.4). Claudia Carillo-Sánchez (WP 20 MFO LAC 1.5), on the one hand, and Charlotte Grégoreski (WP 20 MFO LAC 1.7) on the other analyse how Chile rediscovers itself as a country of immigration with the arrival of Haitians, while at the same time forgetting its past as a country of European immigration, as evoked by Maria Kokkinou in her research on Greek immigrants (WP 20 MFO LAC 1.6). Marie Mallet s paper on the DACA reform in the US (WP 20 MFO LAC 1.8) and Carolina Kobelinsky and Filippo Furri s on migrants dead bodies in Sicilian cemeteries (WP 20 MFO LAC 1.9) move back to Northern destination countries focusing on current exclusive forms of migration management. Finally, the last two papers of this series explore the bearing of policies of forced immobility and return on migrant populations. Veronique Benei, in her description of internal displaced people in Colombia (WP 20 MFO LAC 1.10) reflects on the methodological tools of shared humanity that allow us to enquire into the aftermath and the continuation through other means of structural violence and cruelty. This in turn resonates with Clara Lecadet s account of associative mobilisations triggered by the distress of former African emigrants forcibly expelled from Europe (WP 20 MFO LAC 1.11). Veronique Benei and Thomas Lacroix Annex -Conference programme Migrations in Latin America and the Mediterranean compared: Violence, State cruelty and (Un-)Institutional Resistance Convened by Veronique Benei, Thomas Lacroix and Eduardo Posada-Carbó 12th & 13th of November 2019 Maison Française d Oxford (MFO), Latin American Centre (LAC), Oxford, Institut International d Anthropologie du Contemporain (IIAC/LAIOS) & ECOS-SUD Programme, Paris 12th November 2019 3.00pm-3.30pm: Welcome Véronique Bénéï (CNRS), Thomas Lacroix (MFO) and Eduardo Posada-Carbo (LAC) 3.30pm-5pm: Migratory trends and critical shifts in the Mediterranean Presentation of the English version of the Atlas of Migrations 2019, coordinated by the European and African Migreurop network , by Filippo Furri (University of Montreal, Canada, Ecos-Sud member) and Yasha Maccanico (The Transnational Institute, Bristol University). Chair: Benoît Hazard (IIAC, CNRS) 5.00pm-7.00pm Round table Latin American perspectives on migration The Central American migrants caravans: contesting borders and their governmentalities , by Pascaline Chappart (URMIS/IRD, Paris): The Impact of Haitian Migration in Brazil by Carlos Vargas-Silva (COMPAS, Oxford University) The Venezuelan Migration in Context: Barriers to movement and integration , by Esteban Devis-Amaya (Oxford Brookes) Chair: Andreza de Souza Santos (LAC, Oxford University) Followed by inauguration at LAC 13th of November 2019 9.30am-11.00am: Of S a e iolence: be een ai ing and ilencing Migration and education: Voices and silencing of Haitian immigration in Chile , by Claudia Carrillo (Universidad de Chile, Ecos-Sud member) A migration of no return? Reflections on Greek migrants in Chile , by Maria Kokkinou (EHESS-IIAC, Ecos-Sud member) Chair: Véronique Bénéï (CNRS, IIAC/LAIOS, Paris, Ecos-Sud member) 11.15am-12.45pm: From the local to the global: Institutional scales and stakes The story of a municipal migrants and refugees office in a Santiago de Chile s suburb , by Charlotte Gregoreski (EHESS-IIAC/Universidad de Chile, Ecos-Sud member) The State Control of Identity: Ramifications for DACA recipients , by Marie Mallet (COMPAS, Oxford University) Chair: Juan Luis Ossa (LAC, Oxford University) 2pm-3.30pm: At the borders of humanity: Bodies and moralities. Hosting the dead by migration. The treatment of lifeless bodies in Catania (Sicily) , by Carolina Kobelinsky (CNRS-LESC, Université de Nanterre, Ecos-Sud member) & Filippo Furri (Université de Montréal, Ecos-Sud member) Representations of displacement in Colombia: Humanity, bodies, moralities , by Véronique Benei (IIAC/LAIOS, CNRS-EHESS, Ecos-Sud) The political self-organisation of deportees in the shadow of State politics , Clara Lecadet (IIAC, CNRS-EHESS) Chair: Juanita Leon (St Antony s College, Oxford) 3.30pm-4.30pm: Conclusions and assessment: Thomas Lacroix, Véronique Benei, Carlos Varga Contributors Véronique Benei is a political anthropologist and research director at the National Centre for Scientific Research (CNRS). She currently teaches at the Ecole des Hautes Etudes en Sciences Sociales (EHESS), Paris and is a statutory member of the Interdisciplinary Institute of Contemporary Anthropology (IIAC)/ Laboratory of Anthropology of Institutions and Social Organizations (LAIOS). Having completed her doctorate on the social issue of dowry in India amid the rise of Hindu fascism

  Carrillo holds a Ph.D. in Social Sciences from the Universidad de Chile, and a Master in Education, mention in Curriculum and Educational Community, also from the Universidad de Chile. She was a scholarship holder of the National Commission for Scientific and Technological Research, CONICYT/ANID (Chile) and has been sponsored by the Center for the Study of Conflict and Social Cohesion, COES. She is also a member of the above-mentioned ECOS/ CONICYT programme. Her lines of research concern: migration; sociology of the body and emotions; racism; socio-educational inclusion/exclusion; inequalities; initial and in-service teacher training; curricular and didactic dissemination. Claudia actively participated in the exchange project of the scientific cooperation programme ECOS-CONICYT Spatial Mobilities and Transformations in the Former Urban Peripheries of Latin American Metropolises: Santiago, Bogotá and Buenos Aires (2016) between the Faculty of Architecture and Urbanism, University of Chile and Laboratoire Migrinter, Université de Poitiers, France; in the Nucleus of Research Sociology of the Body and the Emotions, as researcher in charge of the Migrant Bodies Unit (2014-2015) and researcher in the REM Unit: Racism, Foreigners and Migrations (2011-2013) at the Department of Sociology of the FACSO of the University of Chile; in the Fondecyt Regular research project Black immigran in Chile; in Dail prac ice of racialisation/sexualisation funded by CONICYT, as a researcher and doctoral thesis (2013-2015); also as a researcher in the Latin American Network of Studies on Teaching Work (2012-2013) and as a research assistant in the University School Dropout Project of the Department of Psychopedagogy of the Universidad Surcolombiana,USCO, Colombia (2005-2007).Pascaline Chappart, Ph.D. in sociology, is a research fellow at Urmis Paris. Her postdoctoral research deals with the processes of bordering and the reconfiguration of contemporary migrations they produce in Niger and in Mexico. Labelled as "countries of transit by political and academic spheres, Niger and Mexico are situated at the crossroads of migration regimes that appear to be antagonistic if not contradictory. Due to their specific geographical location, these countries are ideal spaces for research on the process of bordering and its socio-political and anthropological impacts. Based on localised case studies in Niger and in Mexico, this crossed perspective questions the current dynamics of outsourcing policies. It also investigates the mapping of migration management as a policy assemblage shaped by the multilateral and local interactions at stake and analyse their effects on the reterritorialization of politics.Esteban Devis-Amaya is a Senior Lecturer in Spanish and Latin American Studies, Department of English and Modern Languages, Faculty of Humanities and Social Sciences at Oxford Brookes University.

  Kokkinou holds a Ph.D. in anthropology from EHESS and is a member of the Institut Interdisciplinaire d An hropologie d Con emporain (IIAC), in Paris. She holds an MA in Social Science, with a specialisation in History of Migration from EHESS and a BA in Social Anthropology and History from the University of Aegean.Her Ph.D. field research was supported with a mobility grant by EHESS, « aide à la recherche du terrain », the A.G. Leventis Foundation and a mobility grant from École Française d Athènes. She coordinates Atelier Balkans an interdisciplinary workshop for doctoral students and young researchers. In her dissertation she examined the role of a specific political and cultural institution (DOME) and its impact on the life of exiled refugees of the Greek civil war(1946)(1947)(1948)(1949) who lived in Bulgaria during socialism. Her research analysed the terms under which the subjects are subordinate to power and the varied content of national identity through the different generations of refugees when exile is ended . Her main research interests embrace, but are not limited to, migration, the Balkans and anthropological theory.More recently, through the ECOS SUD Franco-Chilean programme that she is also a member of, she has started work on the Greeks of Chile s histories and imaginaries of migration.ThomasLacroix is CNRS research fellow in geography. He works on the relationships between immigrant transnationalism and the state. His work initially focused on Indian and North African transnationalism, with a specific interest in their effects on development and integration. His research now focuses on city networks and the building of a local governance of international migrations. He holds a Ph.D. in geography and political sciences (University of Poitiers, 2003). He was awarded a doctoral Marie Curie fellowship at the Centre for the Study of Migrations and Ethnicity (University of Liège, 2002-2003), a postdoctoral Lavoisier fellowship at the Centre Jacques Berque (Rabat, 2004-2005), a postdoctoral Marie Curie fellowship at the Centre for Research in Ethnic Relations (University of Warwick, 2005-2007) and a research fellowship funded by the Volkswagen Foundation the International Migration Institute (University of Oxford, 2008-2011). Thomas Lacroix is former Migrinter deputy director. He is currently associate editor of Migration Studies and research associate at CERI and Migrinter. He is a fellow at the Institut Convergence Migrations. Clara Lecadet holds a Ph.D. in social anthropology and ethnology on the forms of grouping and collective mobilisation of migrants expelled to Mali (EHESS, 2011). She is an anthropologist and CNRS research fellow.Her research focuses on the emergence of a protest movement specific to expellees in Africa and on the forms that their organisation takes in the post-expulsion period. More generally, the history of expulsion policies and practices vis-à-vis foreigners should be considered, as the radical instrument of the distinction between citizens and foreigners in Western countries, but also as factors of social and political transformation in the countries from which immigrants are expelled. Clara is a member of the Air Deportation Project(2017- 2022), supported by the Social Sciences and Humanities Research Council of Canada (SSHRC), led by W.Walters (Carleton University).Her work also addresses the issue of the politicisation of refugees within the camps and how this tends to be overshadowed in the history of refugee camps administered by the Office of the United Nations High Commissioner for Refugees (UNHCR). A research project on the UNHCR archives in Geneva supports this reflection.YashaMaccanico is completing a Ph.D. at the University of Bristol s School for Policy Studies on European Immigration Policies as a Problem: state power and authoritarianism. The development of immigration policy as a means of asserting state power in the EU and its member states . He has been a journalist and researcher monitoring and reporting on EU justice and home affairs policy and the link between EU policies and those enacted in member states with Statewatch since 1998, including the externalisation of migration policies, and co-authored the report The shrinking space for solidarity with migrants and refugees: How the European Union and Member States target and criminalise defenders of the rights of people on the move with the Transnational Institute in Amsterdam in September 2018. Marie L. Mallet is currently a Marie Sk odowska-Curie Researcher at COMPAS. Marie earned her doctorate at Paris Sorbonne in 2013. Her dissertation qualitatively and comparatively analysed Latino political participation in Boston, Los Angeles, and Miami. Marie spent three years in residence at Harvard University as a Fulbright Scholar and a postdoctoral researcher. She has won funding from the University of California at Berkeley, Stanford University, and the Marie Sk odowska-Curie Fellowship.


Sylvester Nhnẹanotnu Osu
email: sylvester.osu@univ-tours.fr

The verb final suffix /-m/ in Ikwere: a rare case of agreement in a language with no agreement system

Keywords: grammatical agreement, category of person, post-verbal nasal consonant, male and female distinction, verb affixes, Igboid languages

Ikwere verbs in sentences can sometimes contain the nasal bilabial consonant /-m/ in the final position. We notice however, that this feature is fairly marginal in the language because the consonant in question mainly occurs where the subject of the sentence is the first person singular. This article claims therefore, that /-m/ marks agreement based on person, meaning that it is evidence of a cross-referencing between the subject noun and the verb. Interestingly, the first person singular does not automatically co-occur with /m/. On the other hand, /-m/ may co-occur with the second and third persons singular as well as the first, second and third persons plural. The aim of this article is to outline the conditions under which this agreement occurs. And while hinging on the absence of noun class agreement or agreement based on gender and number in this language, it is finally suggested that the subject-verb agreement in Ikwere should be regarded as a residual of a more elaborate archaic system which, like the noun class system in some Niger Congo languages (cf. Welmers 1973: 189) including Ikwere, will sooner or later become obsolete.

Introduction

There is no known system of agreement in Ikwere. 1 That is if we consider agreement as "the covariance or matching of features between two separate elements, such as noun and adjective" (Corbett, 1994: 55).

If we take Bantu languages for instance, 2 they have a noun class system. The thing with their kind of noun class system is that it has what [START_REF] Poulos | A linguistic analysis of Venda[END_REF] calls concordial agreement. This means that categories in the language which are grammatically related to the noun, show agreement with the class of the noun by using a concord of that class. 3 Put differently, there is agreement between subject 1 Ikwere is an Igboid language of the Benue-Congo branch. It is spoken by over a million people in Rivers Sate. (Estimate based on 1991 population census, published in the Annual abstract of statistics by Federal Office of Statistics, Nigeria, 1998). IPA symbols are used in Ikwere examples except that dʒ is replaced with j; tʃ with c, and j with y. and ' are nonexplosive, bilabial stops with no velar occlusion. They resemble their explosive counterparts p, b in several ways but differ from them in that they involve no buildup of air pressure behind the occlusion. The symbol gb (replaced in some of my works elsewhere with ) represents a sound that is fully voiced and nonimplosive while kp (replaced in some of my works elsewhere with ' ) is preglottalized, voiced prior to release, and frequently imploded. Although they are also written gb and kp in the current orthography of Ikwere, we must avoid confusing them with labiovelar stops such as those found in Gbe languages. (Interested readers may see [START_REF] Clements | Explosives, implosives, and nonexplosives: the linguistic function of air pressure differences in stops[END_REF]. Tones in Ikwere are indicated as follows: á for High, à for Low, ǎ for Rising, â for Falling, and ↓ á for Down-step High. The tilde under a vowel indicates nasalization. Ikwere has a system of vowel harmony according to which with a few exceptions, all vowels of a word are either [+ATR] or [-ATR]. Hence,lem changes to -lɛm, -g w u to -g w ʊ, -ru to -rʊ and the 3SG o to ɔ. Ikwere also has a system of nasal harmony according to which nonobstruent sounds nasalize if followed or preceded by a nasal vowel -indicated with a tilde-; for instance the underlying form for -nɛm is -lɛm. (See [START_REF] Clements | Ikwere nasal harmony in a typological perspective[END_REF][START_REF] Clements | Nasal harmony in Ikwere, a language with no phonemic nasal consonants[END_REF][START_REF] Osu | Les nasales en ikwere[END_REF] for further discussion). 2 [START_REF] Mohamadou | Classificateurs et représentation des propriétés lexicales en peul: parlers de l'Aadamaawa[END_REF]Mohamadou ( : 20, 2016: 159-160: 159-160) also talks of agreement in Peul, an Atlantic language spoken in the Aadamaawa region in Cameroon (alternate name, Fulani, spoken in Nigeria). And though Mʊ ̀ʊré, a Gur language spoken in Burkina Faso and its environs, also has a noun class system, it does not seem to have any concordial agreement. See [START_REF] Kabore | Essai d'analyse de la langue mʊ ̀ʊré (parler de Waogdgo: Ouagadougou)[END_REF][START_REF] Kabore | Amorphous, seamless vs. polymorphous, seamed entities : -m and -do in Mʊ ̀ʊré noun class system[END_REF].

nouns and other elements of the sentence (verbs, modifiers and pronouns). And this agreement is marked using specific affixes. Each subject noun determines what affix is used. (Watters 2000: 202). Ikwere does not have a noun class system and does not mark any noun class agreement of the sort found in Bantu languages.

Afro-Asiatic languages such as Amharic (see e.g. [START_REF] Negga | Le genre féminin en amharique : une tentative d'interprétation sémantique[END_REF]) and Touareg (see e.g. Aghali 2016), 4 as well as Nilo-Saharan and Khoisan languages (Welmers 1973: 248) are characterized by the fact that they have a gender system. These languages formally mark the difference between masculine and feminine gender. Here again, Ikwere has no gender system and does not grammatically mark the difference between masculine and feminine gender.

Further, Ikwere does not mark any difference between singular nouns (or verbs) and plural nouns (or verbs). In other words, Ikwere has no agreement system based on grammatical number.

However, the Ikwere verb sometimes contains the /-m/ consonant in the final position. A careful analysis reveals that this consonant mainly occurs where the subject of the sentence is the first person singular. We may therefore consider the feature under focus as fairly marginal in contemporary Ikwere.

Interestingly, the first person singular does not consistently co-occur with /-m/. On the other hand, we find cases where /-m/ co-occurs with the second, third persons singular as well as the first, second and third persons plural. How do we account for all this?

In English for instance we have I am as opposed to He is. The verb form indicates that we are dealing with the first person singular in the first case and the third person singular in the second case. Likewise in French, "the pronoun Nous automatically leads to the use of the inflectional morphemeons in the verb chantons. In other words, -ons signifies that the subject noun is the first person plural (Culioli 1968: 28)".

The aim of this article is to outline the conditions under which the agreement between the first person singular subject and the verb takes place.

This article is organized as follows: First I provide data showing that Ikwere has no agreement system whatsoever. The discussion draws on the absence of agreement based on gender and number. Second, I argue that the agreement feature is not totally absent in Ikwere. I show that there are instances where the verb and the first person singular subject must agree otherwise the sentence is not well formed. I also show that such agreement is marked by placing the nasal consonant /-m/ in the final position of the verb. I then examine the various conditions under which this consonant occurs in the verb. Third, I turn to the conditions under which the subject-verb agreement does not apply. Finally, I suggest that the subject-verb agreement in Ikwere, a language with no agreement system, should be regarded as a residual of a more elaborate archaic system that existed in the language.

Ikwere, a language with no grammatical agreement system

The discussion first focuses on the category of number, and then on gender and ends with the category of person.

Lack of agreement based on number

A typical feature of Ikwere nouns (as opposed to verbs) is that they are invariable i.e., they do not change form. Thus, a noun remains morphologically invariable irrespective of the number value of the subject noun, as in ( 1): example, a referent such as "a person" would be categorised differently from a referent such as "an instrument". […]. By the phenomenon of concordial agreement is meant that those categories in the language which have some or other bearing on, or which are grammatically related to the noun, show agreement with the class of the noun by using a concord of that class. So, for example, if a noun is used which belongs to class 2, and an adjective is used with it, then the adjective would incorporate a concord of class 2 as well; and in the same light, if a verb were used with the same noun, then the verb would also contain a concord of class 2." 4 We also find gender systems in many Indo-European languages such as German, French, Portuguese and Russian.

( In a very few cases however, Ikwere distinguishes between unitary and multiple terms. Where such distinction occurs, Ikwere uses different lexical items that do not resemble each other. This is illustrated with kinship terms 5 in table [START_REF] Poulos | A linguistic analysis of Venda[END_REF] below:

5 According to Emenanjo (1978: 208-209), some Igbo dialects (including Onitsha cf. Williamson 1972: 177 and 368)

Lack of gender agreement

Ikwere does not formally assign units to classes on the basis of gender. Thus, examples in (12) do not belong to the masculine, the feminine or the neutral gender. The Amharic language (Afro-Asiatic family) in Ethiopia opposes the 3 rd person masculine singular and the 3 rd person feminine singular as illustrated in (13a) but neutralizes such opposition in the 3 rd person plural as in (13b).

(13a) 3e m.sg əss-u 'he' vs 3e f.sg əss-wa, 'she' (Negga 2016) (13b) ənnä-əss-u, 'they'

The French language (Indo-European, Romance) opposes 3 rd person masculine singular and plural with the 3 rd person feminine singular and plural. As for the English language (Indo-European, Germanic), it distinguishes between the 3 rd person masculine singular he and the feminine counterpart she. Here again, the opposition is neutralized in the 3 rd person plural, just like in Amharic.

The situation is slightly more complex in Telugu (a Dravidian language spoken mainly in the Andhra Pradesh and Telangana states, in India). Telugu distinguishes between the 3 rd person masculine singular and the 3 rd person singular feminine and neuter. It also opposes the 3 rd person plural masculine and feminine with the 3 rd person plural neuter. The masculine singular is marked with the -ḍu suffix while the feminine and neuter counterparts bear the -ei suffix. Further, the masculine and feminine plural have the -ru suffix while the neuter bears the -yi suffix. This is further illustrated in ( 14) to ( 17), drawn from Aikhenvald (2000: 46). ( 14 Quite unlike the languages mentioned above, the m ̀ '1SG', ɪ ̀ '2SG', ò '3SG', à '1PL', ánʊ ̀ '2PL', bɛ ́ '3PL' in Ikwere are not grammatical gender markers. Besides, they can interchangeably refer to a male or female person. It turns out from the discussion so far that Ikwere does not have a grammatical gender system and consequently does not mark any agreement based on gender.

Male and female distinction

Nonetheless, Ikwere does express sexual differences utilizing lexical items that embody biological features of male and female. This is particularly seen in N 1 N 2 relationships. The interesting thing here is that the terms used for such differences depend on whether we are dealing with human beings or not.

Human beings

Sexual differences in relation to the human category are expressed using rùka̰ for male and rìya̰ for female. Thus, the speaker in (18a) wishes to know the sex of a newly-born baby. The speaker in (18b) uses rùka̰ to refer to a male child (a boy) and rìya̰ to refer to a female child (a girl).

(18a) ɔ ̀ mʊ ̀rʊ ̀ kɪ ńɪ . ɔ ̀ mʊ ̀-rʊ ̀ kɪ ńɪ ́ 3SG V.B.

Non human categories

Such differences are however expressed outside the class of humans (i.e., fauna, flora, ailments (sickness), price of commodities, drum sounds, and so on), by using ókḛ for male and éwe ̰ rè for female. See examples in ( 23 In an N 1 N 2 relationship, ókḛ and éwe ̰ rè naturally occur in N 1 position. Besides, they combine with terms irrespective of whether they have or do not have biological sex. A more complete study [START_REF] Osu | Et si les maladies avaient un sexe : l'expression de la différence entre le masculin et le féminin en ikwere[END_REF] shows that ókḛ associates with features such as aggressiveness, danger, urgency, violence, excessiveness and the male sex value while éwe ̰ rè associates with mildness, kindness, melodiousness and the female sex value.

What this means is that the speaker selects these features based on the term ókḛ or éwe ̰ rè combines with.

More importantly, we must take note of the fact that N 1 and N 2 do not contain any affix indicating the agreement between one term and another. Simply put, Ikwere does not mark any agreement based on gender or noun classes.

Agreement based on person

We have seen that Ikwere does not mark agreement based on number and gender. But when it comes to the category of person, we find that in a given utterance, the verb may contain the nasal consonant /m/ in the ultimate position. I claim that this consonant is evidence of the verb-subject agreement. The question is: what are the basic conditions for /-m/ to occur? Conditions for /-m/ to occur in the verb final position For /-m/ to occur, it will require one or more of the following conditions:

(a) The subject of the verb is the first person singular (b) The subject of the verb is the first person singular in the emphatic form and with contrast effect (c) The verb contains the primary verb prefix y-or any of the following suffixes -g w u, -lem and -ru Each of these cases is examined in detail.

(a) The subject of the verb is the first person singular

The speaker in (24) explains why she has put on weight. Consider an altogether different situation: I earlier refused to lend money to a friend who later finds me with a bundle of naira notes and shows his surprise to see me with such amount of money. To calm him down, I can reply:

(b) The subject of the verb is the first person singular in the emphatic form and with contrast effect

The specific thing with the first person singular in the emphatic form and with contrast effect is that the speaker tends to consider the person referred to as a member of a class. He focuses on the person without clearly stating that he excludes the other members of the class with respect to the process in question. This is illustrated in ( 27) to ( 29 As can be seen, the speaker does not in any way specify whether other people are going or not. He talks of his own case, no more, no less.

c) The verb contains a primary verb affix y-(prefix), -gwu, -lem et -ru (suffixes) This is illustrated in (30) -( 35) below. Examples (30), ( 31), ( 33) and ( 34) are affirmative sentences while (32) and ( 35) are negative sentences. They all have the verb final /-m/.

Conditions under which /-m/ does not occur in the verb final position

There are three basic conditions under which the subject-verb agreement does not hold.

a) The subject of the verb is not the first person singular b) The subject of the verb is the emphatic first person singular with the exclusion effect c) The verb contains a primary verb prefix (n-or z-) Each of these conditions is hereafter examined in detail.

a) The subject of the verb is not the first person singular Consider the set of examples below. The subject of the verb is the 2 nd person singular in (36), the 3 rd person singular in (37), the 1 st person plural in (38), the 2 nd person plural in (39) and the 3 rd person plural in (40). Further, the subject is Osi in (41). The absence of /-m/ in all these examples clearly adds weight to my claim that the verb final nasal consonant only occurs with the 1 st person singular. Any attempt to introduce /-m/ while the subject is not the first person singular leads to an unnatural sequence as in ( 42):

b) The subject of the verb is the emphatic first person singular with the exclusion effect

The subject-verb agreement does not hold if the subject of the verb is the emphatic first person singular. This type of use of the first person singular goes together with the exclusion of any other subject or person. Consider ( 43) and ( 44 A sequence like *mé rírʊ ́m á or *má gbárʊ ́m á is just not possible.

c) The verb contains a primary verb prefix (n-or z-)

Among the primary verb affixes, the y-prefix and the -g w u, -lem, and -ru suffixes do co-occur with the verb final /-m/ as shown in (30) to (35). In contrast, the n-and z-prefixes never co-occur with it. This is shown in ( 45) to (48). Note in passing that for reasons yet unknown to me, the z-prefix is realized m-in ( 46) and ( 48) where it comes after the syllabic nasal m, i.e., the 1 st person singular subject. Note also that ( 46) and ( 48) are meant to be affirmative sentences. In an attempt to account for the impossibility of these two prefixes to combine with the verb final /-m/, I first present arguments drawn specifically on Ikwere, and later arguments drawn on related Igboid languages such as Echie, Igbo and Ukwuani.

Reasons for the incompatibility of n-and z-with the verb final /-m/ These two elements have been identified by Worukwo (1983: 59-63) as auxiliary verbs in Ikwere. He thus writes them na and ze respectively. But while the na auxiliary does not exist as an autonomous unit in Ikwere, the verb zɪ 'be' does. This verb implies that someone or something is located somewhere. I assume that zɪ is the same unit Worukwo writes ze.

The basic idea here is that if these two elements earlier served as auxiliary verbs, then they might have lost part or all of their auxiliary status and have gradually come to merge with the main verb, serving this time as prefixes. Thus, in (49) the hypothetical original form should be nà àzǎ 'is sweeping'; in (50), zɪ ̀ àzǎ 'will sweep'. In that case, and quite in line with the rule of no successive vowels or consonants in Ikwere, the first vowel from the left (that of na or zɪ) drops while that of the main verb is maintained, the tones being identical with that of the initial vowel of the main verb stem coalesce with the latter. And we obtain nàzǎ or zàzǎ. All this is illustrated in the set ( 49) to ( 56 It is because n-and z-function as prefixes that they do not combine with the verb final /-m/ in the examples above. Let us consider the following:

(57) Speakers A and B are sisters. A does not want B to eat the food she prepared because B did not do the domestic chores she was asked to do. When their mother returns from the market, she finds A eating alone. She asks to know why B is not eating and gets either of the following answers.

A The one prepared by who, me? No way, she will not eat it.

In (57) (A 2 ), we find ze-, the negative form of zɪ. It is used here to negate the progressive verb form of neri. I assume it is the same z-prefix that is used here as an auxiliary verb. Let's put it this way, in (57) (A 1 ), z-merges with the verb base while in (57) (A 2 ), the n-prefix arrests the merging process. Now compare the following set:

(58) A: byǎ ì zêrí wírí ǹhɛ ̰̀ ɪ ́ ze ̰́ ɛ ḱw ʊ̂ ɔ bʊ ́. In (58) (A) and (B 1 ), z-merges with the verb base èrɩ , whereas in (58) (B 2 ), it doesn't. What we have is the auxiliary form zɛ̂m èrí.

(59) A friend phones me. In (59) (B 1 ), z-contributes to the negative construction of the process, hence z ə -n-ɔ ̀nʊ ̰ and therefore does not have an auxiliary status. In (59) (B 2 ), it equally contributes to the negative meaning construction of the sentence. But in this case, we have the auxiliary form zɛ̂-m n-ɔ ̀nʊ ̰ .

B 1 : m ̀ z ə nɔ ǹʊ ̰́ ńhɛ̰ ɪ ́ nòk w û. m ̀ z ə -n-ɔ ǹʊ ̰́ ńhɛ̰ ɪ ́ n-òk w û 1SG zɪ.V.NEG-PROG-V.B.hear thing 2SG PROG-V.B.speak 1SG FUT.V.NEG-PROG-V.B.
What brings about the use of the sentence in B 1 or B 2 remains very unclear to me at this stage of my investigation. The fact that the two forms coexist tends to indicate that we are at a stage in the evolution of Ikwere where zɪ ̀ is gradually losing its auxiliary function.

Recap (59) (B 1 ):

-merging of the auxiliary with the verb. This leads to the loss of the final m (alternative analysis may claim that the two nasal consonants i.e., the final m in zɛ̂m and the initial n in na merge): zɛ̂mnɔ ̀nʊ ̰ zɛ̂nɔ ̀nʊ ̰ -weakening of the negation marking vowel: z ə nɔ ̀nʊ ̰ with the result that zɛ̂ loses its auxiliary function.

Recap (59) (B 2 ): -The corresponding negative form for zɪ ̀ is zɪ ̀+ɛ̂, realised as zɛ̂ -This negative form agrees with the first person singular subject: zɛ̂m -The verb ɔ ̀nʊ ̰ 'hear' is in the progressive: n-ɔ ̀nʊ ̰ -The auxiliary in the negative form + the verb 'hear' in the progressive: zɛ̂m + n-ɔ ̀nʊ ̰ Arguments drawn from related Igboid languages Auxiliary verbs have been reported to exist in Igboid languages. For instance, a progressive auxiliary marker has formally been identified in Èchiè and Igbo. 9 Reporting precisely on Igbo, Green & Igwe (1963: 141) write: "We have found only one true auxiliary verb. It has the stem na and it is always followed by a participle". 10 Ndimele (2003: 43) also writes: "The progressive aspect in Èchiè is expressed by either the suffix -gha or the auxiliary verb na". Ndimele further reports the use of an auxiliary verb for future time expression in Èchiè. As he puts it (2003: 62), "[…] the auxiliary verb -ga […] expresses future time reference". Emenanjo (1978: 182) considers the low tone auxiliary gà as the (general) future marker in Igbo. In translating gà as 'will', Anyanwu (1998: 139) seems to agree with Emenanjo on future marking in Igbo. Below is a set of examples illustrating the issue under discussion. These examples are taken from Igwe & Green (1964: 35-36) and Okonkwo (1977: 36-38) for Igbo; then from Ndimele (2003: 43) for Èchiè and finally from Williamson (1968: 50, 53) for Ukwuani. I adopt IPA symbols and where necessary, segment words and provide interlinear morpheme by morpheme glosses to make reading a little easier.

The progressive marker in Igbo (cf. Igwe &Green 1964: 35-36 andOkonkwo 1977: 36-38 This set of examples clearly shows that Igboid languages do have auxiliary verbs. In Igbo, the first person singular marker /-m/ occurs in the final position of the auxiliary verb. In other words, if the auxiliary occurs, it takes the final /-m/. But where the auxiliary merges with the stem, meaning in that case that we have only one verb, /-m/ occurs in the final position of the verb. This is quite similar to the case of the progressive marker in Ikwere. It is as if the speaker no longer analyzes n-as an auxiliary.

We can therefore link the absence of the verb final /-m/ in sentences containing the verb prefix n-in Ikwere to the current state of the language change.

It is crucial to note that the final verb /-m/ does not occur in all the examples where one might expect it. In Ukwuani for example, we have in (66) ǹ nàagba ɔsɔɔ ̀ 'I am running' and in (67) ǹ nèete eguù 'I am dancing'. In contrast, we have in (68) adɪ m ̀ nàagba ɔsɔɔ ̀ 'I am not running', in (69) adɪ m ̀ nèete eguù 'I am not dancing'. We notice that the verb final /-m/ occurs in ( 68) and ( 69) where the first person singular is marked with something other than the syllabic nasal m. Further investigations are needed to get a better understanding of the issue at stake here.

The -lêm suffix

The peculiar thing with this verb suffix is that it already contains m in the final position of the affirmative ( 78) -(80) form though not in that of the negative form ( 81 A few remarks are in order here:

In ( 78), there appears to be one final /-m/ on the surface level. But I suspect a coalescence of the final m in -lem and the verb final /-m/. It is to avoid any confusion that might arise from such coalescence that it is realised here with a high tone making this example quite different from ( 79) and (80). In ( 79) -( 81), it is realized with a low tone which I leave unmarked, because it harmonizes with the preceding high-low tone.

Further, comparing ( 81) and ( 82), the verb final /-m/ only occurs in (81). This is quite consistent with the person agreement system since the subject is the first person singular whereas in (82), the subject is the third person singular.

Conclusion

The starting point of this article is the observation that although Ikwere has no system of grammatical agreement, it sometimes uses the verb final /-m/ to indicate a subject-verb agreement in very rare cases and on specific conditions.

The aim of the article therefore has been to map out these specific conditions. And one such condition is that the subject noun must be the first person singular or the first person contrastive singular which automatically brings about the exclusion of any other imaginable person. Another condition is that the verb must contain the y-, -g w u, -lem and -ru affixes but not n-and z-. On this particular point, it was noticed that Ikwere differs to some extent from its sister languages (Echie, Igbo and Ukwuani) in that these two elements function as auxiliaries in these languages whereas only the zprefix can sometimes function as an auxiliary in Ikwere. It was therefore concluded that their incompatibility with /-m/ may have to do with the fact that they are losing their auxiliary function.

The issue at hand is not a central feature in Ikwere in the sense that it concerns only the first person singular subject. We are led to consider one last question: how do we account for the fact that the agreement marking does not extend to other members of the category of person (2 nd and 3 rd persons singular, 1 st , 2 nd and 3 rd persons plural)?

A tentative answer to this question could be that the Ikwere language has been undergoing morphological and syntactic changes.

Thus, in a recent paper [START_REF] Osu | Répartition des noms et préfixation récurrente des noms et des verbes en ɩ kwéré, une langue sans système de classification nominale[END_REF], I show that the commonest type of noun formation in Ikwere is either with an initial vowel or a syllabic nasal which is nothing other than a vocoid. The idea is that such initial vowel and syllabic nasal are reminiscent of a noun class system. This is quite consistent with Welmers' (1973: 190) observation that "[i]n the languages in question here [i.e., some Kwa languages including Yoruba, Igbo and Efik], the noun prefixes have no grammatical function, but their ultimate derivation from a functioning noun class system is virtually an undebatable hypothesis" (Emphasis mine). [START_REF] Williamson | Reconstructing Proto-Igboid Obstruents[END_REF] 2) makes a similar observation: "Most Igboid verb roots are of CV structure, and the most common pattern of nouns is V-CV, where the CV is also interpreted as a root and the initial V-(where V-includes the possibility of a syllabic homorganic nasal) as the remains of a prefix."

In this view, we can hypothesize that Ikwere formerly had a more elaborate system of agreement based on person and perhaps gender, number, and so on. And therefore, the verb final /-m/ can rightly be considered as a residual feature of a system of agreement. *** A French version of this article was presented at the 30 ème colloque du Cerlico, Université de Nantes, 10 & 11 juin 2016.

  (24) m ̀ zɪ -m rɩ ḿé. 1SGV.B.be.LOC-AGR interior I am pregnant.

(

  25) ɪ ́ wa ̰̀ zɪ ḿɛ ńɛ ́ nʊ ́ ḿ rɩ ǵw úm cɩ ḱè ɔ ǵw ɔ . ɪ ́ wa ̰̀ zɪ ́mɛ -nɛ ́ nʊ ́ ḿ rɩ -g w ú-m cɩ ḱè ɔ ǵw ɔ ́ 2SG V.B.forget-NON AFF PFT.INTERROG LINK 1SG V.B.eat-STAT-AGR chike debt Don't forget I owe Chike money? (The verb final /-m/ occurs in the verb rɩ ́gw úm) (26) m ̀ ze ̰̀ rùm ńhɛ̰ dǎ. m ̀ ze ̰̀ -rù-m ńhɛ̰ dǎ. 1SG V.B.go-EFF-AGR thing Daa I went to Daa's house.Examples (24) to (26) clearly show that it is only when the first person singular m occurs in the sentence that the /-m/ consonant occurs in the final position of the verb (see zɪ ̀-m, rɩ ǵw ú-m ɔ ́gw ɔ ́, ze ̰ rùm).

(

  30) m ̀ yɔ ẁɔ ̰́ m máya̰ ńg w ɔ . m ̀ y-ɔ ẁɔ ̰́ -m máya̰ ńg w ɔ ̀ 1SG MOD-V.B.drink-AGR wine palm I drink palm wine (instead). (The speaker first refuses the drink offered him and then proposes an alternative choice). (31) m ̀ ze ̰̀ g w ùm ɛ ḱw ʊ̂. m ̀ ze ̰̀ -g w ù-m ɛ ḱw ʊ̂ 1SG V.B.go-STAT-AGR farm I am going to the farm. (Answer to 'where are you going?') (32) m ̀ ze ̰́ g w ôm. m ̀ ze ̰́ -g w ô-m 1SG V.B.go.NEG-STAT-AGR I refuse to go (so don't just insist). [A friend looked for me but didn't find me at home. I tell him why:] (33) m ̀ ze ̰̀ rùm ńhɛ̰ dǎ. .come-AFF PFT.AGR Alright, I have come (that's what you wanted). (35) ńg w á m ̀ byâlɛ m. ńg w á m ̀ byâ-lɛ -m ̀ alright 1SG V.B.come-NEG.PFT-AGR Alright, I admit, I didn't come.

(

  42) *ò ze ̰̀ rùm ńhɛ̰ dǎ ò ze ̰̀ -rù-m ńhɛ̰ dǎ 3SG V.B.go-EFF-AGR thing Daa *She went to Daa's house. [Reply to a friend looking for Chike.]

(

  45) *m ̀ nèrɩ ḿ wɩ ŕɩ ́ m ̀ n-èrɩ -m wɩ ŕɩ ́ 1SG PROG-V.B.eat-AGR food Intended English equivalent: *I am eating. (46) *m ̀ mèrɩ ḿ wɩ ŕɩ ́ érɩ . m ̀ z-èrɩ -m wɩ ŕɩ ́ érɩ ́ 1SG FUT-V.B.eat-AGR food REDUP Intended English equivalent: *I will eat. (47) *m ̀ nàzǎḿ ńhɛ̰ ̂ m ̀ n-àzǎ-m ńhɛ̰ ̂ 1SG PROG-V.B.sweep-AGR thing Intended English equivalent: *I am sweeping. (48) *m ̀ màzǎḿ ńhɛ̰ ̂ m ̀ z-àzǎ-m ńhɛ̰ ̂ 1SG PROG-V.B.sweep-AGR thing Intended English equivalent: *I will sweep.

  hear thing 2SG PROG-V.B.speak I can't hear you. OR: B 2 : m ̀ zɛ̂m nɔ ǹʊ ̰́ ńhɛ̰ ɪ ́ nòk w û

Table 1 : Unitary vs multiple terms Lack of noun class agreement

 1

	, still have cases where the singular is opposed to the plural, especially among kinship terms. Consider:
	Singular		Plural
	ògòlì	'married woman'	ìgòlì	'married women'
	òkolo	'young man	ìkolo	'young men
	okènyè	'old man'	ikènyè	'old men'
	òkpòro	'woman'	ìkpòro	'women'
	ɔ hà	'people'	ɪ hà	'peoples'

(11) rʊ ́mʊ ̀tàkɪ ŕɪ ́ nète ̰́ éꜜrí. rʊ ́mʊ ̀-tàkɪ ́rɪ ́ n-ète ̰́ érí children-small PROG-V.B.-dance dance Small children are dancing.

  , in N 1 N 2 relationships, rùka̰ (roughly 'male') and rìya̰ (roughly 'female') occur in the N 2 position. They help to determine the sexual value of N 1 as the latter value is initially unspecified.

	ɔ ̀	mʊ ̀rʊ ̀		rùka̰ /rìya̰
	3SG	V.B.deliverr-EFF	male/female
	She delivered a boy/a girl.
	Consider the following:
	(19) ńye ̰́ rùka ̰̀ , byǎ. ńye ̰́	rùka ̰̀ byǎ
	person.adult	male V.B.come
	Sir, (please) come!
	(20) ńye ̰́ rìya ̰̀ , byǎ. ńye ̰́	rìya ̰̀	byǎ
	person.adult	female	V.B.come
	Madam, (please), come.
	ńhɛ̰	ò	we ̰̀ -rù		bʊ ́	ótù	we ̰́ né	rùka ̰̀	kpɔ ý
	chose	3SG V.B.have-DAT	V.B.be.IDF	one collateral male	only
	He has just one brother/cousin.
	ńhɛ̰	ò	we ̰̀ -rù		bʊ ́	ótù	we ̰́ né	rìya ̰̀	kpɔ ý
	chose	3SG V.B.have-DAT	V.B.be.IDF	one collateral female	only
	He has just one sister/cousin.

deliver-EFF what What did she deliver (meaning 'what is the sex of the baby she delivered')? (18b) ɔ ̀ mʊ ̀rʊ ̀ rùka̰ /rìya̰ .

Actually(21) ńhɛ̰ ò we ̰̀ rù bʊ ́ ótù we ̰́ né rùka ̰̀ kpɔ ý. (22)

ńhɛ̰ ò we ̰̀ rù bʊ ́ ótù we ̰́ né rìya ̰̀ kpɔ ý.

  ):

	(23)
	ókḛ ákɔ m	'male malaria' 7	versus	éwe ̰̀ rè ákɔ m	'female malaria'
	ókḛ rʊ ́kw à	'male drum'	versus	éwe ̰̀ rè rʊ ́kw à	'female drum'
	ókḛ kóm	'male cat'	versus	éwe ̰̀ rè kóm	'female cat'
	ókḛ àtàbàlà ókḛ ńwɔ ̰́	'male tilapia' 'male child'	versus versus	éwe ̰̀ rè àtàbàlà éwe ̰̀ rè ńwɔ ̰́	'female tilapia' 'female child'

  ):(27) mɛ ɛ bʊ ́m ńwɔ ̰́ wɔ ǵà yáa bʊ ́ ńwɔ ̰́ òríjí.

	(29) mɛ ɛ ze ̰́ g w òm ó. mɛ ɛ	ze ̰́ -g w ò-m		ó
	1SG.CONTR.EMPH V.B.go-STAT.NEG-AGR	SFP
	As for me, I am not going.
	mɛ ɛ 1SG.CONTR.EMPH V.B.be.IDF . -AGR child bʊ ́-m ńwɔ ̰́	wɔ ǵà yǎ Woga him V.B.be.IDF bʊ ́	ńwɔ ̰́ child	òríjí Oriji
	I am Woga's child, (while) she is Oriji's child.
	(28) mɛ ɛ byàwám ó.
	mɛ ɛ	byàwá-m	ó
	1SG.CONTR.EMPH	V.B.come-AGR	SFP
	As for me, I'm going.

[

  One can say to a friend who isn't careful with the way he spends money.] (36) ɪ ́ wa ̰̀ zɪ ́mɛ ńɛ ́ nʊ ́ ɪ ́ rɩ ǵw ú cɩ ḱè ɔ ́gw ɔ ́ ?The question reading here is certainly brought about by the situational context and the speaker's intonation.

	ɪ ́	wa ̰̀ zɪ ḿɛ -nɛ ́			nʊ ́	ɪ ́	rɩ -g w ú	cɩ ḱè	ɔ ǵw ɔ ́
	2SG	V.B.forget-NON AFF PFT.INTERROG	LINK	2SG V.B.eat-STAT chike debt
	Have you forgotten that you owe Chike some money? (The focus here is the verb rɩ ́gw ú).
	(37) ò ze ̰̀ rù ńhɛ̰ dǎ. ò ze ̰̀ -rù	ńhɛ̰	dǎ
	3SG	V.B.go-EFF	thing	Daa
	S/he went to Daa's house. [Reply to a friend who wanted to see Chike.]
	(38) à zɪ ̀ nʊ ́ rɩ ḿé ɔ ́rɔ ̀ wɩ ŕɩ . à zɪ ̀	nʊ ́	rɩ ḿé	ɔ ŕɔ ̀	wɩ ŕɩ ́
	1PL	V.B.be.LOC	LINK	interior house	food
	We are in the kitchen. [A reply to a neighbour searching for us.]
	(39) ànʊ ̀ ze ̰̀ rù ńhɛ̰ dǎ. ànʊ ̀ ze ̰̀ -rù	ńhɛ̰	dǎ
	2PL V.B.go-EFF	thing	Daa
	Did you go to Daa's house?
	(40) bè ze ̰̀ rù ńhɛ̰ dǎ. bè ze ̰̀ -rù	ńhɛ̰	dǎ
	3PL V.B.go-EFF	thing	Daa
	They went to Daa's house.
	(41) ósì zɪ ̀ nʊ ́ rɩ ḿé ɔ ŕɔ ̀ wɩ ŕɩ . ósì zɪ ̀	nʊ ́	rɩ ḿé	ɔ ŕɔ ̀	wɩ ŕɩ ́
	ósì	V.B.be.LOC	LINK	interior	house food
	Osi is in the kitchen. [A reply to a neighbour who came looking for Osi.]

  ) below.

	(51) bè	n-ètí		ḿbí.
	3PL na-V.B. play		cards
	3PL PROG-V.B. play	cards
	They are playing cards.
	(52) bè	z-ètí	ḿbí.
	3PL zɪ-V.B. play	cards
	3PL FUT-V.B. play	cards
	They will play cards.
	(53) à	n-ɔ tʊ ́		míꜜní.
	1PL na-V.B. knock	water
	1PL PROG-V.B. knock	water
	We are fetching water (from the well).
	(54) à	z-ɔ tʊ ́		míꜜní.
	1PL zɪ-V.B. knock		water
	1PL FUT-V.B. knock	water
	We will fetch water (from the well).
	(55) ò	n-ògbú		ígbúgbú	kè	ézí.
	3SG	na-V.B.kills		pains	LINK bigness
	3SG	PROG-V.B.kills pains	LINK bigness
	It pains too much.
	(56) ò zògbú í ígbúgbú ó
	ò	z-ògbú	í	ígbúgbú	ó
	3SG	FUT-kill	you	pains
	(49) ɔ ̀	n-àzǎ		ńhɛ̰ .
	3SG	na-V.B.sweep	thing
	3SG	PROG-V.B.sweep	thing
	S/he is sweeping the house.
	(50) ɔ ̀	z-àzǎ		ńhɛ̰ .
	3SG	zɪ-V.B.sweep	thing
	3SG	FUT-V.B.sweep	thing
	S/he will sweep the house.

SFP

It will pain you, just know it.

  ʔ ɛ ̰́ ʔ ɛ ̰̀ , m ̀ zɛ̂m èrí, rʊ ́hw ɔ ́ yágbág w ɔ̂m àgbà.

	byǎ		ì	z-êrí		ǹhɛ ̰̀	ɪ ́	ze ̰́	ɛ ḱw ʊ̂	ɔ bʊ ́
	V.B.come.INJ 2SG zɪ-V.B.eat.NEG	thing 2SG V.B.go	farm	in question
	V.B.come.INJ 2SG FUT-V.B.eat.NEG thing 2SG V.B.go	farm	in question
	Tell me, won't you eat before going to the farm?
	B 1 : m ̀ mèrí érí. m ̀ z-èrí 8		érí
	1SG	zɪ-V.B.eat	REDUP
	1SG	FUT-V.B.eat	REDUP
	Of course I will.
	B 2 : ʔ ɛ ̰́ ʔ ɛ ̰̀	m ̀	zɛ̂-m		èrí	rʊ ́hw ɔ ́	y-ágbá-g w ɔ̂-m	àgbà
	no	1SG zɪ.NEG-AGR	V.B.eat stomach MOD-V.B.open-STAT.NEG.1SG	REDUP
	no	1SG FUT.NEG-AGR V.B.eat stomach MOD-V.B.open-STAT.NEG.1SG	REDUP
	No, I won't eat, I am not yet hungry.

  )

	(73) ɔ-gà nza̍ . (64) ɔ-zàghà ʊlɔ . ɔ-zà-ghà ɔ-gà		nza̍	ʊlɔ ̀
	3clitic-sweep-PROG 3SGclitic-aux	house pr-sweep
	S/he is sweeping the house. S/he will sweep.
	(65) ɔ-nà-àzà ʊ ̀lɔ . ɔ-nà-àzà The auxiliary future marker in Ukwuani ʊ ̀lɔ ̀ (cf. Williamson 1968: 50, 53)
	3clitic-aux-pr-sweep		house
	S/he is sweeping the house. (74) mà àba àgba ɔsɔɔ . mà àba àgba The progressive marker na in Ụkwụanị ɔsɔɔ ̀ 1SG FUT.AUX V.B.run race
	(cf. Williamson 1968: 50, 53) 13 I will run
	(75) mà àbeète eguù. (66) ǹ nàagba ɔsɔɔ . ǹ nà-agba mà àba 1SG AUX.PROG-V.B.run ète 1SG FUT.AUX V.B.dance	eguù ɔsɔɔ ̀ race dance
	I am running I will dance
	(60) (67) ǹ nèete eguù. anà m ̀ àzʊ anʊ̍ . a-nà m ̀11 àzʊ ǹ nè-ete (76) ejeko̍ m jààgba ɔsɔɔ . ejeko̍ m jà-àgba 1SG AUX.PROG-V.B.dance 1SG-jeko̍ 1SG FUT.AUX-V.B.run anʊ̍ eguù dance I am dancing I will not run	ɔsɔɔ ̀ race
	1SG-PROG 1SG buy I am (was) buying (buy, bought) meat. meat (61) anà m ̀ ekè anʊ̍ . a-nà m ̀ ekè anʊ̍ (77) ejeko̍ m jèète eguù. (68) adɪ m ̀ nàagba ɔsɔɔ . adɪ m ̀ nà-agba ejeko̍ m jè-ète 1SG-V.B.be LOC.NEG 1SG AUX.PROG-V.B.run eguù 1SG-jeko̍ 1SG FUT.AUX-V.B.dance dance I am not running I will not dance	ɔsɔɔ ̀ race
	1SG-PROG	1SG divide	meat
	I am (was) sharing meat (69) adɪ m ̀ nèete eguù.
	adɪ			m ̀	nèete	eguù
	(62) ana m ata. 12 1SG-V.B.be LOC.NEG	1SG AUX.PROG-V.B.dance	dance
	a-na I am not dancing m	ata
	1SG-PROG 1SG	chew
	I am chewing. The auxiliary future marker ga in Igbo
	(cf. Okonkwo 1977: 36-38)
	(63) ana m eri.
	a-na (70) aga m ata.	m	eri
	1SG-PROG 1SG manger a-ga m ata
	I am eating. 1SG-FUT 1SG chew
	I will chew.
	The progressive markers gha and na in Èchiè
	(cf. Ndimele 2003: 43) (71) aga m eri.
	a-ga	m	eri
	1SG-FUT	1SG eat
	I will eat.
	The auxiliary future marker ga in Echie
	(cf. Ndimele 2003: 62)
	(72) ɔ-gà nri.
	ɔ-gà		nri
	3Sclitic-Aux		prefix-eat
	S/he will eat.

  .B.eat-V.B.finish-AFF PFT They have finished eating (you can now tidy up the table). (81) sétě nʊ ́ m ̀ yɔ ́wɔ ̰́ nɛ̂m máyá ńg w ɔ . I have not yet had palm wine. [In a party. One of two friends suggests that they leave. The second one gives reasons why he doesn't want them to leave.] (82) sétě nʊ ́ ɔ ́ yɔ ẃɔ ̰́ nɛ̂ máyá ńg w ɔ .

	bè	rɩ -k w ó-lêm
	3PL
	sétě		nʊ ́	m ̀	y-ɔ ẃɔ ̰́ -nɛ̂-m		máyá	ńg w ɔ ̀
	V.B.wait.INJ	LINK	1SG MOD-V.B.drink-NON AFF PFT.NEG-AGR		wine	palm
	Hold on, sétě	nʊ ́	ɔ ́	yɔ ẃɔ ̰́ nɛ̂	máyá ńg w ɔ ̀
	V.B.wait.INJ	LINK 2SG MOD-V.B.drink-NON AFF NEG PFT	wine	palm
	Hold on, he has not yet had palm wine.
							) -(82). Consider the
	following:
	(78) m ̀ rɩ ḱw ólêḿ. m ̀ rɩ -k w ó-lêm-ḿ
	1SG	V.B.eat-V.B.finish-AFF PFT-AGR
	I have finished (we can go now).
	(79) ò rɩ ḱw ólêm. ò rɩ -k w ó-lêm
	3SG	V.B.eat-V.B.finish-AFF PFT
	S/he has finished eating (you can now tidy up the table).
	(80) bè rɩ ḱw ólêm.

V

Poulos (1990: 5) writes: "Nouns are put into classes according to the form of their prefix. In other words, speakers of these languages use a system of prefixes to classify the "constituents" of the universe. So, for

See Kadima (1969: 82) for fuller discussion of noun classes in Bantu languages. But see[START_REF] Delplanque | Accord et non-accord du qualificatif dans les langues gur[END_REF] for a different view.

A male kind of malaria is severe in nature. It causes unbearable pains. A female kind goes together with bearable pains. A male kind of drum has a high-pitched, harsh sound. It is beaten in a community to signal a state of emergency while the female kind has a bass low-pitched sound that is soft and melodious.

Recall that the z-prefix is realized m-if preceded by the syllabic nasal m.

The verb final /-m/ occurs in examples (68), (69), (76) and (77) among others. I need to recall at this point that my main purpose here is to show that the presence of the auxiliary of the progressive (n-) or the auxiliary of the future (z-) renders the verb final /-m/ compatible with the first person singular.

Abbreviations


published or not. The documents may come     Mitochondrial activity studies (MTT test) D0, D3, D7, D14, D21 and D28 3D printing process Bio-extrusion Polymerization

Effect of 3D bio-extrusion and polymerization processes during cartilaginous substitutes production using alginate-based bio-ink

Océane

Figure 1 :

 1 Figure 1 : Mitochondrial activity of the MSCs in the different substitutes with a concentration of 1 or 2 M cells/mL. Data are shown as mean ± SD. The effect of the different steps were tested by a two-way ANOVA. Then, the effect of the cells density was globaly tested by a one-way ANOVA. # p < 0.05, # # p < 0.01, # # # p < 0.001. (n=4)

Figure 2 :

 2 Figure 2 : Mitochondrial activity of the MSCs traited or not with TGF-β1 over time. Data are shown as mean ± SD for each time, the effect of TGF-β1 is compared to ITS only by a two-way ANOVA. * p < 0.05, * * p < 0.01, * * * p < 0.001. The effect of the cells density was then globaly tested by a oneway ANOVA. # p < 0.05, # # p < 0.01, # # # p < 0.001. Results : The mitochondrial activity slightly increases in the first days, similarly for the two cell concentrations. From D7, mitochondrial activity remains stable up to D28 for the two cell concentrations without significant difference between the two culture conditions, ITS or TGF-ß1.

This work was supported by « Direction générale des Armées (DGA) », Grant/Award Number N°ANR 16-ASTR-0021, « Fondation de l'Avenir pour la Recherche Médicale Appliquée », Grant/Award Number N°AP-RM-16-042 and « Université de Lorraine -Région Alsace-Champagne-Ardennes-Lorraine 2016 », Grant/Award Number N°AAP-002-037 Objectif ) to produce cartilaginous substitutes containing 1 million (1M) or 2 millions (2M) of cells/ml. Mitochondrial activity of the MSCs at D3, D7, D14, D21 and D28 in the conditions ITS or TGF-β1 : Tissue engineering : Cartilage -Layered -Non-vascularized -Non-innervated → Limited self-healing potential Lesions -Chondral → No repair -Osteochondral → Fibrocartilaginous repair