Liang Ma

Damien Chablat

Fouad Bennis

Wei Zhang

A New Dynamic Muscle Fatigue Model and its Validation

Keywords: Muscle fatigue, muscle fatigue index, muscle fatigue model, maximum endurance time, maximum voluntary contraction, virtual reality

Musculoskeletal disorder (MSD) is one of the major health problems in physical work especially in manual handling jobs. In several literatures, muscle fatigue is considered to be closely related to MSD, especially for muscle related disorders. In addition to many existing analysis techniques for muscle fatigue assessment and MSD risk analysis, in this paper, a new muscle fatigue model was proposed. The new proposed model reflects the influence of external load, workload history, and individual differences. This model is simple in mathematics and can be easily applied in realtime calculation, such as the application in realtime virtual work simulation and evaluation. The new model was mathematically validated with 24 existing static models by comparing the calculated METs, and qualitatively or quantitatively validated with 3 existing dynamic models. The proposed model shows high or moderate similarities in predicting the METs with all the 24 static models. Validation results with the three dynamic models were also promising. The main limitation of the model is that it still lacks experimental validation for more dynamic situations.

Relevance to industry

Muscle fatigue is one of the main reasons causing MSDs in industry, especially for physical work. Correct evaluation of muscle fatigue is necessary to determine work-rest regimens and reduce the risks of MSD.

INTRODUCTION

Musculoskeletal disorder is defined as injuries and disorders to muscles, nerves, tendons, ligaments, joints, cartilage and spinal discs and it does not include injuries resulting from slips, trips, falls or similar accidents [START_REF] Maier | Work-related musculoskeletal disorders[END_REF].

From the report of HSE [START_REF] Hse | Self-reported work-related illness in 2004/05[END_REF] and the report of Washington State Department of Labor and Industries (Safety and Health Assessment and Research for Prevention (SHARP), 2005), over 50% of workers in industry have suffered from musculoskeletal disorders. There are numerous of \risk factors" associating with the work-related MSDs, such as physical workload factors [START_REF] Burdorf | Exposure assessment of risk factors for disorders of the back in occupational epidemiology[END_REF], psychosocial factors [START_REF] Bongers | Psychosocial factors at work and musculoskeletal disorders[END_REF] and individual factors [START_REF] Armstrong | A conceptual model for work-related neck and upper-limb musculoskeletal disorders[END_REF].

According to the analysis in Occupational Biomechanics [START_REF] Chaffin | Occupational Biomechanics[END_REF] and in several literatures [START_REF] Armstrong | A conceptual model for work-related neck and upper-limb musculoskeletal disorders[END_REF][START_REF] Buckle | The nature of work-related neck and upper limb musculoskeletal disorders[END_REF], "physical work requirements and individual factors determine muscle force and length characteristics as a function of time, which in turn determines muscle energy requirements. Muscle energy requirements in turn can lead to fatigue, which then can lead to muscle disorders." Overexertion of muscle force or frequent high muscle load is the main reason for muscle fatigue, and further more, it results in acute muscle fatigue, pain in muscles and the worst functional disability in muscles and other tissues of human body. Hence, it is necessary for ergonomists to find an efficient method to assess physical exposures to muscles and to predict muscle fatigue in work design stage.

In order to assess physical risks to MSDS, several ergonomics tools were developed and most of them were listed, classified and compared in paper [START_REF] Li | Current techniques for assessing physical exposure to work-related musculoskeletal risks, with emphasis on posture-based methods[END_REF]. Observational methods for posture analysis, such as Posturegram, Ovako Working Posture Analyzing System (OWAS), Posture Targeting and Quick Exposure Check for work-related musculoskeletal risks (QEC), were developed for analyzing whole body postures. In all these four methods, posture is taken as one of the most important factors to assess the physical exposure. In the former three methods, body posture is categorized into different types with different risk levels according to recorded position. The differences between these methods are the rules to classify the body positions. In QEC method, posture of different body parts is scaled into different exposure levels. In combination with posture, other physical factors like force, repetition and duration of movement, are also taken into consideration to assess physical workload in OWAS and QEC methods. In spite of these general posture analysis tools, some special tools are designed for specific parts of human body. For example, Rapid Upper Limb Assessment (RULA) is designed for assessing the severity of postural loading for upper extremity. This method has the same concept of OWAS, but particularly suited for sedentary jobs [START_REF] Mcatamney | Rula: A survey method for the investigation of work-related upper limb disorders[END_REF]. It uses ranking system to rate different postures, different movements and repetition/duration of the task. The similar systems include HAMA (Hand-Arm-Movement Analysis), PLIBEL (method for the identification of musculoskeletal stress factors that may have injurious effects) and so on [START_REF] Stanton | Handbook of Human Factors and Ergonomics Methods[END_REF]. \In general, these observational methods are mainly posture-based. They are relatively inexpensive to carry out, and the assessments can be made without disruption to the workforce" [START_REF] Li | Current techniques for assessing physical exposure to work-related musculoskeletal risks, with emphasis on posture-based methods[END_REF]. Similar to these methods for posture analysis, there is one tool available for fatigue analysis: muscle fatigue analysis (MFA) [START_REF] Rodgers | Handbook of Human Factors and Ergonomics Methods[END_REF]. This technique is developed by Rodgers and Williams to characterize the discomfort described by workers on automobile assembly lines and fabrication tasks [START_REF] Rodgers | Recovery time needs for repetitive work[END_REF]. In this method, each body part is scaled into four effort levels according to its working position, and meanwhile the duration of the effort and frequency are both scaled into four effort levels. The combination of the three factors' levels can determine "priority to change" score. The task with high priority score needs to be analyzed and redesigned to reduce the MSD risks [START_REF] Stanton | Handbook of Human Factors and Ergonomics Methods[END_REF].

After listing these available methods, physical exposure to MSD can be evaluated with respect to intensity (or magnitude), repetitiveness and duration [START_REF] Li | Current techniques for assessing physical exposure to work-related musculoskeletal risks, with emphasis on posture-based methods[END_REF]. While these methods can be used to assess physical jobs, there are still several limitations. At first, even just for lifting job, the evaluation results of five tools (NIOSH lifting index, ACGIH TLV, 3DSSPP, WA L&I, Snook) for the same task were different, and sometimes even contradictory [START_REF] Russell | Comparing the results of five lifting analysis tools[END_REF]. That is because these techniques are lack of precision and their reliability of the system is a problem for assessing the physical exposures due to their intermittent recording procedures [START_REF] Burdorf | Exposure assessment of risk factors for disorders of the back in occupational epidemiology[END_REF]. Second, most of the traditional methods have to be carried out onsite; therefore there is no immediate result from the observation. It is time consuming for afterward analysis. Further more, subjective variability can influence the evaluation results even using the same observation methods for the same task [START_REF] Lamkull | The influence of virtual human model appearance on visual ergonomics posture evaluation[END_REF]. At last, only intermittent posture positions and limited working conditions are considered in these methods, which means that they are suitable for analyzing static working process and they are not less suitable to estimate the MSD risks into details.

Besides these objective posture analysis tools, there are several self-report methods to assess the physical load or body discomfort, such as "body map" [START_REF] Corlett | A technique for assessing postural discomfort[END_REF], rating scales [START_REF] Borg | Borg's Perceived Exertion and Pain Scales[END_REF], questionnaires or interviews [START_REF] Wiktorin | Validity of self-reported exposures to work postures and manual materials handling[END_REF] and checklists [START_REF] Corlett | Evaluation of Human Work[END_REF]. These tools are also important because ergonomists have to concentrate themselves on the feeling of the workers. Several authors even insist that "If the person tells you that he is loaded and effortful, then he is loaded and effortful whatever the behavioral and performances measures may show" [START_REF] Li | Current techniques for assessing physical exposure to work-related musculoskeletal risks, with emphasis on posture-based methods[END_REF]. For muscle fatigue, perceived rating exertion (PRE) and Swedish Occupational Fatigue Inventory (SOFI) based on PRE were developed to rate the workload in practice [START_REF] Borg | Borg's Perceived Exertion and Pain Scales[END_REF][START_REF] Ahsberg | Perceived quality of fatigue during different occupational tasks development of a questionnaire[END_REF][START_REF] Ahsberg | Perceived fatigue during physical work: an experimental evaluation of a fatigue inventory[END_REF]. SOFI consists of five aspects: lack of motivation, sleepiness, physical discomfort, lack of energy, and physical exertion, and it is used to measure fatigue as a perception of either mental or physical character [START_REF] Ahsberg | Perceived fatigue during physical work: an experimental evaluation of a fatigue inventory[END_REF]. The concept of perceived exertion and the associated methods for measuring fatigue is: "the human sensory system can function as an efficient instrument to evaluate the work load by integrating many peripheral and central signals of strain" [START_REF] Borg | Handbook of Human Factors and Ergonomics Methods[END_REF]. These subjective assessments of body strain and discomfort have been the most frequently used form due to the ease of use and apparent face validity. But subjective ratings are prone to many influences. This kind of approach has lower validity [START_REF] Burdorf | Comparison of methods for the assessment of postural load on the back[END_REF] and reliability [START_REF] Wiktorin | Validity of self-reported exposures to work postures and manual materials handling[END_REF].

In order to evaluate the human work objectively and quickly, virtual human techniques have been developed to facilitate the ergonomic evaluation, such as Jack [START_REF] Badler | Simulating Humans[END_REF], ErgoMan [START_REF] Schaub | A computer-aided tool for ergonomic workplace design and preventive health care[END_REF], 3DSSPP (Chaffin,1969), Santos (VSR Research Group, 2004;[START_REF] Vignes | Modeling muscle fatigue in digital humans[END_REF]) and so on. They have been used in the fields of automotive, military, aerospace and so on. These human modeling tools are mainly used for visualization to provide information about body posture, reachability and field of view etc [START_REF] Lamkull | The influence of virtual human model appearance on visual ergonomics posture evaluation[END_REF]. The effort of combining these virtual human tools with existing posture analysis methods have been done. For example, in the literature [START_REF] Jayaram | Introducing quantitative analysis methods into virtual environments for real-time and continuous ergonomic evaluations[END_REF], a method to link virtual environment (Jack) and quantitative ergonomic analysis tools (RULA) in real time for occupational ergonomics studies was presented, and it allowed that ergonomic evaluation could be carried out in real time in their prototype system. But until today, there is still no muscle fatigue index available in these virtual human tools for dynamic working process. It is necessary to develop the muscle fatigue model and then integrate it into the virtual human software to evaluate the muscle fatigue and analyze the physical work into details.

For objectively predicting muscle fatigue, several muscle fatigue models and fatigue index have been proposed in literatures. In a series of publications [START_REF] Wexler | A mathematical model that predicts skeletal muscle force[END_REF]Ding et al., 2000aDing et al., ,b, 2003)), Wexler and his colleagues have proposed a new muscle fatigue model based on Ca 2+ cross-bridge mechanism and verified the model with stimulation experiments, but it is mainly based on physiological mechanism and it seems complex for ergonomic application due to its amount of variables. For example, only for quadriceps, there are more than 20 variables to describe the muscle fatigue mechanism. Further more, there are only parameters available for quadriceps, and it is hard to integrate it for full body application. This model was integrated into virtual soldier research (VSR) system to simulate the movement of legs by lifting loads using quadriceps [START_REF] Vignes | Modeling muscle fatigue in digital humans[END_REF], and the results showed Wexler's Model could predict muscle fatigue correctly, but it still needs to be generalized for the other muscles. Another muscle fatigue model based on force-pH relationship is developed by [START_REF] Giat | A musculotendon model of the fatigue profiles of paralyzed quadriceps muscle under FES[END_REF]. This fatigue model was obtained by curve fitting of the pH level with time t in the course of stimulation and recovery. Taku [START_REF] Komura | Calculation and visualization of the dynamic ability of the human body[END_REF][START_REF] Komura | Creating and retargeting motion by the musculoskeletal human[END_REF] have employed this model in computer graphics to visualize the muscle capacity and then to evaluate the feasibility of the movement. They did not evaluate the muscle fatigue of the whole working process. Meanwhile in this pH muscle fatigue model, although the force generation capacity can be mathematically analyzed, the influences on fatigue from muscle forces are not considered. Rodriguez proposed a half-joint fatigue model in the publications (Rodriguez et al., 2003a,b,c), more exactly a fatigue index, based on mechanical properties of muscle groups. This fatigue model was used to calculate the fatigue at joint level: two half-joints, and the fatigue level is expressed as the actual holding time normalized by maximum holding time of the half-joint.

With this model, it is able to apply a posture optimization algorithm to adapt human posture during a working process dynamically when fatigue appears, but it cannot predict individual muscle fatigue due to its half-joint principle because the movement of joint is activated by several muscles. The maximum holding time equation of this model was from static posture analysis and it is mainly suitable for evaluating static postures. In [START_REF] Liu | A dynamical model of muscle activation, fatigue, and recovery[END_REF], a dynamic muscle model is proposed based on motor units pattern of muscle, and in this model, two phenomenological parameters were introduced to construct the muscle model to describe the activation, fatigue and recovery process. But there were just parameters available under maximum voluntary contraction situation of right hand which is rare in manual handling work, and further more, there is still no application of this model in ergonomics field.

In order to analyze the physical work in details and predict the physical exposures, especially muscle fatigue, a new method, concerning the overall dynamic working process, should be developed to assess and predict the potential MSD risks, objectively and easily. In this paper, we are going to propose a dynamic muscle fatigue model and a fatigue index with consideration of muscle load history and personal factors. This fatigue model is going to be validated with comparison of the previous static endurance time models and three dynamic muscle fatigue models. At last, we are going to present an application framework of our dynamic fatigue model to evaluate physical work.

DYNAMIC MUSCLE FATIGUE MODEL

In order to construct the new fatigue model and fatigue index, like in the mentioned ergonomics methods for physical exposures, external load of the muscle with time and the strength capacity of the muscle are involved in our model. These factors can represent the physical risk factors mentioned before: the external load exposed to the muscle with time can cover the information of the intensity (or magnitude), repetitiveness, and duration of force; and the muscle strength capacity can be determined individually and can be treated as personal factor. Thus, the muscle force history (external factor) and maximum voluntary contraction (MVC) (internal factor) are taken to construct our muscle fatigue model. MVC is defined as "the force generated with feedback and encouragement, when the subject believes it is a maximal effort" [START_REF] Vollestad | Measurement of human muscle fatigue[END_REF]. The effect of MVC on endurance time is often used in ergonomic applications to define the worker capabilities or to decide the work-rest rhythm [START_REF] Garg | The effect of maximum voluntary contraction on endurance times for the shoulder girdle[END_REF]. In our model, MVC describes the maximum force generation capacity of an individual muscle.

Our new objective fatigue index is trying to evaluate muscle fatigue by describing the human's perception of muscle fatigue. In general, the fatigue evaluation result is a growth function with external load. In the same period, the larger the external load is, the more fatigue people can feel. The same relation is also used in posture analysis methods with higher risk levels for heavier external load. Meanwhile, the fatigue is a growth function with the reciprocal of muscle force capacity. The smaller the capacity, the quicker the muscle gets fatigue. Further more, fatigue is a growth function with the time. The longer a load is applied, the more fatigue people can feel. This is represented in conventional methods as frequency and duration of physical task. If the fatigue is expressed in differential equation, the influence of time can be excluded. The fatigue index is proposed in Eq. ( 1). The parameters used in the equations are listed and described in Table 1.

) ( ) ( ) ( ) ( t F t F t F MVC dt t dU cem load cem  (1)
Eq. ( 1) can be explained as follows:

 F cem describes

 

(2)

Eq. ( 2) can be explained by the motor unit activation pattern of muscle. Muscle is made of muscle fibers. Force and movement of muscle are produced by contraction of muscle fibers controlled by nervous-system command [START_REF] Liu | A dynamical model of muscle activation, fatigue, and recovery[END_REF][START_REF] Vollestad | Measurement of human muscle fatigue[END_REF]. The basic functional unit of muscle is motor unit, which consists of a motoneuron and the muscle fibers that it innervates. The motoneurons supply the control signals from central nervous-system (CNS) to the muscle fibers. A muscle consists of many motor units, the number of which varies depending on the size and function of the muscle. Each motor unit has different force generation capability, and different fatigue and recovery properties. Generally, they can be divided into three types: type I is slow twitch motor units with small force generation capability and low conduction velocity, but a very high fatigue resistance; type IIb is of fast-twitch speed, high force capacity, but fast fatigability; type IIa, between type I and type IIb, has a moderate force capacity and moderate fatigue resistance. The sequence of recruitment is in the order of: I IIa  IIb [START_REF] Vollestad | Measurement of human muscle fatigue[END_REF]. For a specified muscle, larger F load means more type II motors are involved into the force generation, as a result, the muscle gets fatigue more rapidly, as expressed in Eq. ( 2). F cem represents the non-fatigue motor units of the muscle. In the progress of force generation, the number of type II motors is getting smaller and smaller due to fatigue, while the number of the type I motor units remains almost the same due to its high fatigue resistance, the decrease of F cem with the time is getting slower, as expressed in Eq. ( 2) by term

F cem (t)/MV C .
The integration result of Eq. ( 2) is Eq. ( 3).

   t load du MVC u F k cem MVCe t F 0 ) ( ) ( (3)
Assume that F(t) is:

du MVC u F t F t load   0 ) ( ) ( (4)
MVC is a constant value of a muscle or a muscle group for an individual person during a certain period, so we can change Eq. (3) into Eq. ( 5). If external load F load is constant, assign C = F load /MVC, then F(t) = Ct, and Eq. ( 3) can be further simplified into Eq. 5. This constant case can occur during static posture and static load.

kCt t kF cem e e MVC t F     ) ( ) ( (5)
The subjective perception is a function below, which is closely related to MVC and F load (t). MVC can represent the personal factors [START_REF] Chaffin | Occupational Biomechanics[END_REF], and F load (t) is the force exerted on the muscle along the time and it reflects the influences of external loads Eq. ( 6).

) 0 ( 2 ) ( 2 2 1 2 1 ) ( kF t kF e k e k t U   (6)
In this model, personal factors and external load history are considered to evaluate the muscle fatigue. It can be easily used and integrated into simulation software for real time evaluation especially for dynamic working processes. This model needs to be mathematically validated and ergonomic experimentally validated.

STATIC VALIDATION

Validation Result

Our dynamic muscle fatigue model is based on the hypothesis on the reduction of the maximum exertable force capacity of muscle. It should be able to describe the most special case: static situations. In static posture analysis, there is no model to describe the reduction of the muscle capacity related to muscle force, but there are several models about maximum endurance time (MET) which is a measurement related to static muscular work. MET represents the maximum time during which a static load can be maintained [START_REF] Elahrache | Percentile values for determining maximum endurance times for static muscular work[END_REF]. The MET is most often calculated in relation to the percentage of the voluntary maximum contraction (%MVC) or to the relative force (f MVC = %MVC/100) required by the task. These models, cited from [START_REF] Elahrache | Percentile values for determining maximum endurance times for static muscular work[END_REF], are listed in Table 2.

In our dynamic model, suppose that F load (t) is constant, then it represents the static situation. MET is the duration in which F cem falls down to the current F load . Thus, MET can be figured out in Eq. ( 7) and (8).

) ( ) ( 0 ) ( t F MVCe t F load du MVC u F k cem t load     (7) MVC MVC load load kf f MVC t F k MVC t F MET t ) ln( ) ( ) ( ln      (8)
In order to analyze the relationship between MET obtained from our dynamic model and the other models, two correlation coefficients are calculated. One is Pearson's correlation r in Eq. ( 9) and the other one is intraclass correlation ICC in Eq. 9) within between within between

       n n n n n n n B B A A B B A A r 2 2 ) ( ) ( ) )( ( (

MS p MS MS

MS ICC ) 1 (     ( 10
)
Since Huijgens' model (General model) was developed using data from Rohmert (General model), only Rohmert general model is drawn in Fig. 1 and Fig. 2. And Sjogaard's model was constructed using data from Hagberg (Elbow model) and

Rohmert (General model), Sjogaard's model is excluded in Fig. 1 and Fig. 2.

Discussion

From the comparison results of the static validation, it is obvious that MET model derived from our dynamic model has a great linear correlation with the other experimental static endurance models, and almost all the Pearson's correlation r are above 0.97. Despite the high linear correlation, there are still large differences between the dynamic model and other MET models. These differences include mainly the following influencing factors:  Experiment methods and model construction: In order to measure MET, several tools, such as subjective scales and EMG, are involved. The subjective scales and the variability of participants can bring significant differences into MET result [START_REF] Elahrache | Percentile values for determining maximum endurance times for static muscular work[END_REF]. Further more, the MET models are constructed using different mathematical models, mainly power function and negative exponential function. But the negative exponential function can not describe the two asymptotic tendencies: a tendency towards infinity for low %MVC and a tendency towards zero for values bordering on 100%, %MVC. In fact, all the parameters of the other MET models are fitted from experimental data, and due to the limitations of sampling amount, the MET models can be quite different, especially for the two extreme %MVCs.

 Muscle group and posture variability: MET models for different muscle groups are different, and the statistics results showed that there is a significant difference between the MET values for the back/hip and the MET values for the upper limbs, for the same %MVC value [START_REF] Elahrache | Percentile values for determining maximum endurance times for static muscular work[END_REF].

In addition, MET models are mathematically different even for the same muscle group under different postures. Different muscle group has different anatomical structure and different complexity. In the same muscle group, the involvement of muscle elements can be changed significantly, which can also explain the significance between different postures. In the literature [START_REF] Garg | The effect of maximum voluntary contraction on endurance times for the shoulder girdle[END_REF], the influences of shoulder postures were discussed. It indicated that different posture would produce different moments and loads on the same muscle group, thus it would cause different MET curves.

 Interindividual variability: from the figures, it is obvious that the differences of MET values are greater for low %MVC than those for high %MVC. The significant interindividual differences in MET [START_REF] Elahrache | Percentile values for determining maximum endurance times for static muscular work[END_REF] can cause the differences.

From ICC column, it shows high similarity between the dynamic model and several MET models: for elbow and hand models, 5 out of 7 are higher than 0.90; for general model, 3 out of 5 (Huijgens' and Sjogaard's model are not counted) ICC values are higher than 0.85. But it also shows moderate or low similarity with the other MET models. For example, with the back/hip models, ICC varies from -0.057 to 0.9447. The explanation is: ICC correlation is significantly influenced by the complexity of the anatomical structure. In shoulder and back/hip of human body, the anatomical structure is in a much more complex way than in the elbows and hands.

For this reason, in these experimental models, the measurement of MVC and MET is an overall performance of the complex muscle group, but not MET of an individual muscle or simple muscle group. Meanwhile, even for one muscle group, in Fig. 7, the differences between the experimental models for hip/back are greater than MET models for other muscle groups, e.g. in elbow models (Fig. 5). It can also be explained by the complexity of the anatomical structure. In different working conditions (for example, different postures), the engagement of the muscles in the task in the hip/back of human body and the contraction of muscle are different as well, which can further influence the experimental result.

In conclusion, the dynamic model is validated by comparing with 24 static MET models. The validated result shows high similarity with many of the static MET models, while moderate similarity with a few static MET models, possibly due to complex muscle structure, mathematical function limitation, and measurement condition.

DYNAMIC VALIDATION

Validation result

Static validation results have shown promising result for general static load and even for some specific body parts. But static procedures are still quite different from dynamic situations, thus our dynamic model need to be examined with the other dynamic models. For this objective, the following part is going to verify our dynamic model through comparison with some existing muscle fatigue models, quantitatively or qualitatively.

In the literature [START_REF] Freund | A dynamic model of the forearm including fatigue[END_REF], a muscle fatigue model was proposed and integrated into a dynamic model of forearm. In this model, the muscle was treated like a kind of reservoir, and force production capacity S 0 reduces with the time that the muscle is contracted. S 0 varies between 0 and the upper limits of the muscle force S 1 . In this model, the recovery and decay rates depend on S l -S 0 and muscle force S (Eq.

( contraction force, so it represents higher muscle load. From Fig. 9, it is clear that the higher the stimulation frequency is, the larger the force can be generated by the muscle. The larger the peak force (higher frequency) is, the faster the curve declines, and the quicker the muscle gets fatigue. This trend is similarly represented in our dynamic model by Eq. ( 2).

Though qualitatively verified, it is impossible to verify our dynamic model with Wexler's model quantitatively due to the way in which Wexler's model was obtained.

Wexler's model is experimentally validated in stimulation trials, and all parameters were calculated from external stimulation experiment. But the muscle simulated in external manner, the motor recruitment mechanism could be different from that controlled by CNS. In external manner, all the motor units of muscle are stimulated simultaneously, creating a larger force than voluntary contraction and get fatigue more rapidly [START_REF] Vignes | Modeling muscle fatigue in digital humans[END_REF].

In the literature [START_REF] Liu | A dynamical model of muscle activation, fatigue, and recovery[END_REF], the dynamic model of muscle activation, fatigue and recovery was proposed. This model is based on biophysical mechanisms: motor units pattern in 2. The generated force is proportional to the activated motor units in the muscle. The brain effort B, fatigue property F and recovery property R of muscle can decide the number of activated motor units. The relationship is expressed by Eq. ( 12). The parameters in this equation are explained in Table 3.

F A uc F A F F A uc A M M M M M R M F dt dM M R M F BM dt dM         0 (12)
When t = 0 under the initial conditions of M A = 0, M F = 0, M uc = M 0 , we can have Eq. ( 13) and ( 14).

Ft

Ft A e e M t M                          1 ) 1 )( 1 ( 1 ) ( ) 1 ( 0 (13) Ft uc e M t M    0 ) ( (14)
In the new dynamic fatigue model, we assume that there is no recovery during physical work, and the workers are trying their best to finish the task which means the brain effort is infinitely high. In this assumption, we set γ=0 and βinfinity, then Eq.

(15) represents the motor units which are not fatigued in the muscle. The activated motors M A (t)/M 0 and the motors in rest M uc (t)/M 0 represent the muscle force capacity.

We can simplify the sum of Eq. ( 13) and ( 14) to Eq. ( 15) which do have the same form of our dynamic model Eq. ( 5).

Ft Ft Ft uc A e e e M t M M t M                          1 1 ) 1 )( 1 ( 1 ) ( ) ( ) 1 ( 0 0 (15)
This fatigue model has been experimentally verified in [START_REF] Liu | A dynamical model of muscle activation, fatigue, and recovery[END_REF]. In the experiment, each subject performed an MVC of the right hand by gripping a hand grip device for 3 min. And the fitting curve from the experimental result has almost the same curve of our model in MVC condition (Fig. 10). In this model, F and R are assumed to be constant for an individual under MVC working conditions. There is no experimental result for F and R under the other load situations, thus this muscle fatigue model can only verify our model in MVC condition.

Discussion

APPLICATION IN DIGITAL WORK EVALUATION FRAMEWORK

After mathematical validation of the proposed dynamic model, a virtual reality framework is going to be constructed to apply the fatigue index in virtual environment for digital work evaluation.

The function structure of the framework is shown in Fig. 11. From Section 2, necessary information for dynamic manual handling jobs evaluation consists of posture, external load, repetition, and duration of load. Motion capture techniques can be applied to collect the motion information. The rest information can be analyzed from haptic interfaces or force feedback systems. All the information, such as motion information, force history, and interaction events, is further processed into Objective Work Evaluation System (OWES). The output of the framework is evaluation results of the physical work, and one of these output results is muscle fatigue evaluation.

The prototype of this framework has been constructed for ergonomics studies to measure the performance in two-dimensional panel control [START_REF] Wang | An integrated simulation system for human factors study[END_REF]. The new dynamic fatigue index is going to be integrated into the prototype system to evaluate fatigue of physical works.

CONCLUSIONS

In this paper, a new muscle fatigue model was proposed. Based on this model, a new fatigue index was proposed. The new model was mathematically validated with 24 existing static models by comparing the calculated METs and qualitatively or quantitatively validated with 3 existing dynamic models. The proposed model shows high or moderate similarities in predicting the METs with all the 24 static models.

Validation with the three dynamic models was also promising. The new proposed model reflects the influence of external load, workload history, and individual differences. It is simple in mathematics and can be easily applied in realtime calculation, such as the application in virtual work simulation and evaluation.

The main limitation of the model is that it still lacks experimental validation for more dynamic situations.

ACKNOWLEDGEMENT

This research was supported by the EADS and by the Region des Pays de la Loire (France) in the context of collaboration between the Ecole Centrale de Nantes (Nantes, France) and Tsinghua University (Beijing, P.R.China).

( 10 )

 10 . r indicates the linear relationship between two random variables and ICC can represent the similarity between two random variables. The closer r is to 1, the more the two models are linearly related. The closer ICC is to 1, the more similar the models are. MS between is the mean square between different MET values in different f MVC values; MS within is the mean square within MET values in different models at the same f MVC level. p is the number of models in the comparison. In our case, we compare the other models with our dynamic model one by one, thus p equals to 2. The calculation results are shown in Table 2 and Fig. 1 to 8.



  )). The constants α and β were obtained by fitting the solution using experimental results from static endurance time test. In this model, muscle force is taken into consideration as a factor causing muscle fatigue, and further more, muscle force production capacity S 0 was proposed just like in our dynamic model F cem to describe the capacity of the muscle after performing certain task. But in this model, the force production capacity and the muscle force are decoupled with each other, which is different in our model. In this model, the same concept was employed to describe the fatigue mechanism of muscle. dynamic muscle fatigue model based on Ca 2+ cross-bridge mechanism can also verify our dynamic model qualitatively. This model can be used to predict the muscle force fatigue under different stimulation frequencies. The stimulation frequency is to simulate the control commands of CNS for muscle contraction. The higher frequency stimulation, the more muscle motors are activated to generate

  Through dynamic validation, our dynamic model is either qualitatively or quantitatively verified with the other three existing muscle fatigue models. The fatigue model for the forearm used the same conception like in our fatigue model: the muscle force capacity is related to muscle force with time. Wexler's model based on Ca 2+ cross-bridge shows the reduction of the muscle force during the time under different stimulation frequencies, the reduction of the muscle capacity shows the same trend like in our muscle fatigue model. With comparison to the active motor model, the muscle force can be expressed in the same form under extremity situation. But in the active motor model, only parameters are available for MVC contraction case. The active motor does not supply further validation for other load situations.

  the capacity of the muscle during the contraction progress at a time instant t. It falls down during the contraction process because the muscle gets fatigue in a continuous contraction.  F load (t)/F cem (t) is the relative load at a time instant t which describes the current muscle force normalized the capacity of the muscle at a time instant t. MVC/F cem (t): reciprocal of muscle force capacity, this term represents the inverse percentage capacity of the tester at a time instant t relative to the initial MVC. With development of time, this term gets larger while the F cem (t) falls down, and accordingly the increase of fatigue index becomes slower.

	This term describes the relation of fatigue index with normalized relative
	load.
	 ) ( ) ( ) ( t MVC dt load F t F t dF cem cem

Meanwhile, the capacity of muscle (current muscle force capacity) F cem (t) is changing with time due to the external muscle load. The larger the external load, the faster F cem (t) decreases. The differential equation for F cem is proposed in Eq. (

2

), which is the basic function of the new dynamic fatigue model.

TABLES FIGURES


Michael Saidani

Harrison Kim

Bernard Yannou

CIRCULARITY INDICATORS AND TOOLS FOR PRODUCT DESIGN: A WEB-BASED VISUALIZATION AND SELECTION TOOL

Circularity indicators and tools for product design: A web-based visualization and selection tool

Michael Saidani, Harrison Kim, Bernard

DESIGN TOOL SHOWCASE

A new add-on for facilitating and monitoring circular product design is made available on the c-indicators webplatform: https://c-indicators.000webhostapp.com/index.php. This online platform, including two web-based tools -the C-Indicators Advisor and the Circularity Potential Indicator -has been first introduced during the 2019 edition of the Design Tool Showcase [START_REF] Saidani | C-indicators: a web-based platform to monitor and improve the circularity potential of products[END_REF]. Meanwhile, the number of circular economy indicators (covering different aspects and scales of the circular economy) continued to rise, leading both to utility and fuzziness for industrial practitioners. Among this plethora of recently developed circularity indicators, it is key to identify the ones that are particularly adapted to be deployed during the design process to foster design for circularity, as a means of operationalizing sustainability in product development. While a previous contribution started to investigate the potential value of applying four circular economy-related indicators during the design process to augment the circularity potential of products [START_REF] Saidani | Product circularity indicators: what contributions in designing for a circular economy?[END_REF], the present research is more systemic and identified twelve productfocused c-indicators coming with computational tools that could be insightful and practical during the design process.

To support designers and engineers in the selection of adequate product-centric c-indicators, these twelve ad hoc cindicators are mapped on a generalized five-step engineering design process (x-axis), including: (i) requirements definition, (ii) conceptual design, (iii) detailed design, (iv) designs comparison, and (v) product monitoring and communication [START_REF] Saidani | Design for Product Circularity: Circular Economy Indicators With Tools Mapped Along the Engineering Design Process[END_REF]. Also, these c-indicators and their associated assessment tools are ranked according to their level of complexity or time required to be computed, in order to further inform designers or engineers, 1 Contact author: msaidani@illinois.edu who might use such tools for the first time, on their usability and user-friendliness. To facilitate the identification, selection, and deployment of ad hoc product-level c-indicators, a visualization web-based tool is proposed, mapping on an interactive twodimensional chart these c-indicators. This web-based application has been developed using the JavaScript library React. The user interface and interactive chart have been implemented using Plotly: http://circulareconomyindicators.com/design.php. This web-based app is expected to be linked with an updated version of the database of circular economy indicators from the C-Indicators Advisor, as well as to provide and display infoboxes (and use cases, if any) for selected c-indicators.

During the 2021 Design Tool Showcase, concrete examples -using e.g., the Circularity Potential Indicator (CPI), the Circular Economy Indicator Prototype (CEIP), or the (Circularity Calculator) CC -will be given on how these cindicators can guide the circular design of products at different steps of the design process. Promising perspectives for future research will also be discussed and illustrated, such as the integration, compatibility, and combination of c-indicators with other design methods and tools, like life cycle assessment software or computer-aided design programs.

Keywords

  : Design for circular economy, circularity indicators, product design, design process, web-based tool.

	ILLUSTRATIONS OF THE TOOL
	www.circulareconomyindicators.com/design.php
	NOMENCLATURE
	CC	Circularity Calculator
	CCET	Concept Circularity Evaluation Tool
	CEIP	Circular Economy Indicator Prototype
	CET	Circular Economy Toolkit
	CIAM	Circular Index from CirculAbility Model
	CP	Circular Pathfinder
	CPI	Circularity Potential Indicator
	MCI	Material Circularity Indicator
	MCPD	Material Circularity in Product Design
	MDI	Material Durability Indicator
	PCI	Product Circularity Indictor
	RPI	Reuse Potential Indicator


Life While Waiting. Experiencing the Asylum Application in France

Life While Waiting. Experiencing the Asylum Application in France.

Carolina Kobelinsky

In: (2021). Mercier D., Zuñiga V., Doraï K., El Miri M. and Peraldi M. (eds.) Experiencing Ruptures in Migration. The ordinary and unexpected journeys of global migrants. London: Transnational Press London, UK, It is half past ten, Edona and Gazmadh Bashe 1 finish their coffee, sat around the small round table, next to the bed that was already made. Gazmadh goes downstairs to the first floor where the social workers' offices are, to look for his mail. He then goes to the ground floor, at the entrance of the reception centre for asylum seekers (CADA), where smokers sometimes group together. He meets Omar, corridor neighbor, and a "Russian of the fourth floor" whose name he ignores. They talk about the weather, go out to smoke, two cigarettes. They say hello to those who come in, to those who go out. Edona, on the other hand, goes to wash cups in the shared kitchen. I go with her. There is already a lady preparing the lunch. Back in the room, Edona turns on the television, mutes it, takes a small French dictionary and a paperback which she borrowed from the municipal library. She systematically looks for the definition of all the words she doesn't know, asks them to me "to be sure" and then writes them on a blue pad. Gazmadh comes back, Edona asks him if there was some mail. "No". He puts back the TV sound and stretches out on the bed. Edona continues to read. I go out. (…) At noon twenty, I knock again at their door. Edona still reads and Gazmadh went down to smoke. She suggests preparing the meal, we then take onions, tomatoes, rice, some spices and we go to the common kitchen where three other people do the same task. We go back to the room, Gazmadh is back, we set the table and we eat while discussing entertainment activities organized by the CADA, and Albania football championship. Gazmadh prepares some coffee, we eat tangerines. He goes down to smoke and we sit in front of the television, Edona takes a look at all the channels, stops on an American TV series dubbed in French. When the broadcast is over, Edona goes to do the dishes in the kitchen, I prepare some tea. Edona comes back with Anna, Omar's wife, she sits down with us. They have been in CADA for three months and are in the room next door. She tells us the bad news that her husband received on his family who stayed in Palestine (…) She leaves, I go out with her (…) Around four in the afternoon, I am back, Edona and Gazmadh are sitting around the small round table. What are you doing? "Nothing, as usual", answers Edona. I propose them figs that a Somalian resident had just offered me, we discuss. Gazmadh goes downstairs to smoke a cigarette, then goes back up. "The watch does not move forward", he says staring at her. It is only five fifty. (field notes, CADA, 12/10/04). This day of October 2004 is similar to many others. No much happens, no milestone, no particular activity. And nevertheless, this ethnographic vignette reports an essential dimension of the asylum application experience as lived by Edona and Gazmadh Bashe: the waiting and, more particularly, the experience of a motionless temporality.

In the following pages, I will explore Edona and Gazmadh Bashe's waiting during the asylum procedure and their life in a CADA, situated in the Parisian suburbs where I met them in April, 2004. The chapter draws on four interviews carried out with Edona, and on numerous informal conversations with both spouses during afternoons in the shelter, dinners at my home or outings to the library located at the George Pompidou Center in Paris, which Gazmadh particularly liked. Instead of building the analysis around Edona and Gazmadh Bashe life story, I rather suggest operating a kind of cross section in their path and focusing on their waiting practices and experiences bounded by a precise time and space, but which go beyond CADA and the asylum procedure. Waiting is moreover recurring in migrants' trajectories, every time in a different form and intensity, involving a singular relationship to time, but also to space.

The Bashe spouses perceive the pending decision concerning their refugee status and their life in the shelter, as the possibility to breathe again after a wandering period; then, as the boredom and inactivity's daily experience, as well as an obstacle to the realization of their projects. But they will develop particular activities, out of CADA, to fight inactivity and shade off the imposed temporality. This multiple experience of waiting -sometimes lived as an advantage, at times heavy to deal withmeets the one of most of the asylum seekers I met during my ethnographical investigation, carried out during 26 months between 2003 and 2008, in CADA shelters around Paris. Two brief bends are imperative before exploring Edona and Gazmadh Bashe's practices and experiences, one concerning what produces such waiting time -the asylum bureaucracy -and the other one on the place where it spreads -the reception center. Regarding the procedure, the one who requests asylum has to demonstrate that the motives which urged him or her to come in France are in agreement with those stipulated by the 1951's Geneva Convention, which defines a refugee as a person who: "owing to well-founded fear of being persecuted for reasons of race, religion, nationality, membership of a particular social group or political opinion, is outside the country of his nationality and is unable or, owing to such fear, is unwilling to avail himself of the protection of that country; or who, not having a nationality and being outside the country of his former habitual residence as a result of such events, is unable or, owing to such fear, is unable to return to it"2 .

After submitting a request to the administrative office, the person obtains a renewable residency until the end of the procedure. The file is examined by the French Office for the Protection of Refugees and Stateless Persons, which most of the time summons the applicant to an interview before giving its decision. If the request is rejected -what happens in most of the cases -it is possible to draft an appeal to what was called at the time of this study the Refugees Appeals Board3 . This institution is in charge of examining the case and of summoning the applicant to a public hearing in front of three judges, before they take the decision. In case the initial rejection is confirmed, the person cannot renew his or her residence permit anymore and is from that very moment considered in an irregular situation, removable at any time from the French territory. There are few possibilities of turning the situation in favor of the applicant. If a legal problem is spotted -which is not frequent -, it is possible to present, through a lawyer, an appeal to the Council of State and to the Court of Cassation. During the review period, no residence permit is freed to the asylum seeker, the decisions of removal from the territory being able to be executed. In case of cancellation, the appeal is sent back to the Refugees Appeals Board for a new examination. It is also possible to ask for the case reopening to the administrative instance, but it requires the applicant to produce new elements in order to adduce fears in case of return in the country of origin. In this case, the Office delivers a certificate of re-examination and the Prefecture has to extend the residence permit. The case starts again the path towards the Office, then possibly towards the appeal's institution.

Funded by the French State, CADAs are daily managed by NGOs or companies which employ social workers, educators, lawyers, to take care of the social and legal follow-up of the candidates for refugee status, who are accommodated there for the entire length of asylum procedure. The hosting offered by CADAs can be "split" in isolated apartments, outside the building where the CADA administration sits, or "collective", in shelter type buildings. I conducted my field research in collective structures -more numerous than those offering a scattered accommodation. These structures were created in 1991, two months after the effective application of a circular forbidding de facto the right to work for asylum seekers.

CADAs are ambiguous institutions. They offer a particular form of hospitality that associate assistance, control and confinement. Professionals bring a legal advice allowing to work out the application, increasing asylum seekers' chances to obtain the refugee status or, at least, subsidiary protection4 . They also take care of the necessary steps to reach the universal asylum, or of what is now called « subsidiary protection ». This latter is allowed to individuals who may face inhuman or degrading treatment or punishment in their countries, regardless of the persecution cause. A lot weaker than the refugee status, subsidiary protection is submitted to an annual reassessment from authorities of the French Office for the Protection of Refugees and Stateless Persons.

healthcare coverage 5 and school the residents' children. They sometimes also bring support to people who share their sufferings with them. But on the other hand, the social workers have to control the asylum seekers' moves. Even if these ones can go back and forth from the shelter, according to the internal rules of these institutions, which newcomers necessarily have to sign, any absence of more than a day must be reported to the team of the CADA, and absences involving many days must be authorized by the direction. The asylum seekers' mail is monitored, as it transits to the social workers' office. A photocopy of all the official letters is kept, whether they are questions linked to the asylum procedure, to the renewal of their temporary residence permit, to their health coverage or to fines for fraud in transport. In certain shelters, the team organizes regular rooms "visits" to verify the current building condition and the good agreement between neighbors, but to also take a look at the cleanliness, the housekeeping and the residents' habits. In other shelters, inspection is replaced by meetings with a social worker acting as the "corridor advisor", who ensures, I will be explained, the "good relationship and the premises' respect". Besides, a more or less formal form of control is exercised on a daily basis. Comments expressed by social workers on the joke mode, such as "Ahh, sir, I'm pleased to see you, I had almost forgotten your face!" recall the residents' absenteeism during entertainment activities, or their lack of investment in the meetings organized by CADA. Other comments also informally expressed and on a playful tone, point the late arrivals to collect the mail or the tokens allowing getting to the laundry. They remind people staying in shelters that they are observed and their attitudes monitored. A more formal control is exercised towards the visits that residents can possibly receive in their rooms, which must in certain institutions, be announced in the entrance of the building or with social workers.

CADAs are not spaces of imprisonment as detention centers, waiting areas at airports or prisons. They can however be considered as structures of confinement which participate (with the mentioned spaces) in a migrants' containment device which has been developed for several decades in France as elsewhere in the European Union [START_REF] Kobelinsky | L'accueil des demandeurs d'asile[END_REF]Kobelinsky and Makaremi 2009).

Time as a resource

In May 2003, Edona and Gazmadh Bashe decide to leave their home town, Korçë, in the South of Albania. "The violence had gotten out of hand", they were afraid. Edona's injury motivated their departure. Not knowing what to do, they first leave for Tirana, the capital of the country. Then, they spend a few weeks with some relatives in a remote village of the north, "to think and try to see more clearly", as Gazmadh explained to me during a form of protection was above 70 % in CADA vs 16 % at the national level (FTDA 2005: 6). The skimming done at the moment of candidates' selection for the allocation of places in CADAsbecause there are not many places for all the applicantscan also constitute an explanation for these achievements. 5 Social security benefit allowing the access to health insurance for any individual who has regularly resided in France for more than three months and who is not yet covered by the social security regime. conversation years later. They will have gone "almost everywhere in Albania" before being able to find 5.000 dollars asked by the smuggler who helped them come in France. Hidden in a truck with about ten other people, they crossed Montenegro and the border with Bosnia-Herzegovina; then, always hidden behind the truck, they took the boat to the port of Bari. Once in Italy, they continued the trip for a few hours before taking another vehicle which drove them to Charenton-le pont in France. From their arrival in December, they especially remember the cold and the nights spent in the Parisian subway. One day, Edona calls out to a young woman in the street, she speaks to her in English, they discuss for a long time and the lady recommends them to call 115 6 to find a place where to sleep. After three days of fruitless attempts, they are allowed to stay during some nights in a hotel. They tell me that they were then able to stay during two months in a hospital, sleeping in a "small bed". They ask for asylum 7 in January 2004 and arrive at CADA three months later, eleven months after leaving Korçë. The social worker introduces me to Edona Bashe three days after their arrival at the shelter. She tells me she feels "light", since she arrived there she slept better, she felt "peaceful". She had tough times while trying to speak French, so we began to talk in English and Italian. A few months later, we meet to discuss in her room. She spoke French enough well to maintain a conversation, she learned it in self-taught. She could not attend the class proposed by CADA because she had to regularly go to the hospital. She had one recent surgery and was about to have two others. "When we went the first time to Thérèse's office [their social worker], I told her that I needed a doctor for my face. She made calls, it was very good, I went to the hospital and everything is good, Gazmadh comes with me every time. I feel better" (interview with Edona Bashe, shelter, 10/14/2004). Edona's long dark hair always covered the left-hand side of her face. She tried to hide a deformed eye, a swollen cheek and an impressive reddish scar, which was the reason that urged her to leave Korçë, she told me one day. She felt better since the first surgery and the regular treatments helped her a lot; she was relieved to be able to take care of her health. The arrival to CADA gave, indeed, to Edona and Gazmadh, ways to physically and psychologically recover from what they suffer on their path. They "were happy and relieved" to have a place where they can to sleep and get some money to meet their needs 8 . They had 6 Nation-wide emergency phone-number at the district level, for homeless people. 7 At that time, the Albanian Republic was not yet in the list of so called « safe » countries, established by the administrative board of the French Office for the Protection of Refugees and Stateless Persons. A country is considered « safe » if, by law, it « ensures respect for the principles of freedom, democracy and the rule of law, as well as human rights and fundamental freedoms ». Since December 2013, Albania was introduced in that list and its people can no longer apply to stay for asylum reasons. They can, however, request a study of their application in a priority procedure, which will then be evaluated in a period of 15 days after the application had been submitted. In addition, since June 2014, Albania is part of the European Union. 8 It's a living allowance paid by CADA. Its amount varies according to the services given by the shelter and the number of family members. Edona and Gazmadh received 267 euros per month. 8 It's a living allowance paid by CADA. Its amount varies according to the services given by the shelter and the number of family members. Edona and Gazmadh received 267 euros per month. a small room Edona carefully decorated. They shared the kitchen and the bathroom with other asylum seekers' families coming from Russia, Angola, Palestine, Cameroon and Sri Lanka. "We are happy to be here, of course it is not our house, but we are not anymore in hotels, in the hospital … I do not know how long that is going to take but we stay here several months in a row, that is really good (…) We are lighter, relieved. We learn on the questions of papers, CMU [universal healthcare coverage], meetings, the asylum. Thérèse and all the advisors help us understand how all this work" (interview with Edona Bashe, shelter, 10/25/04). "Lightness" and "relief" about which Edona speaks -terms also used by other interlocutors -can only be understood according to their journey of forced circulation. From the day they leave their place of residence in Albania until their arrival at the shelter, their singular journey meets in many aspects, trajectories made of escapes and wandering of all the people I met. CADA offered to Edona and Gazmadh Bashe the feeling of being protected. First times in the shelter provide a temporary form of stability. As they have time ahead of them, this period is often perceived as the opportunity to learn the meanders of the French bureaucracy, as Edona said. The "know-how" of the social workers is well appreciated, as it covers a whole set of domains often underestimated by the newcomers in France: social rights opening, orientation towards healthcare professionals and, fundamental for the residents, the construction of the asylum narrative and, in addition for many asylum seekers, the language learning. If Gazmadh admitted to have more difficulty with French, Edona, in other hand, dedicated at least two hours a day to make grammar exercises with a borrowed book or to read and study the words she did not understand, as the vignette -at the beginning of this chapter-illustrates. She also watched TV to improve her understanding. "We, we bought the TV cheap and it is very practical because I hear and I learn French. I improved a lot since we have the TV, I also listen to the radio, it also helps me but it is more for music!" (Conversation with Edona Bashe, shelter, 10/25/04). Five months after their arrival at CADA, they are scheduled to attend an interview at the French Office for the Protection of Refugees and Stateless Persons. Their application for asylum was rejected a few months later. Apart from the disappointment, it was urgent for them to appeal before the Refugee Appeals Boardin thirty days after they received the notification of rejection. During these weeks, their social worker provided them with a "big moral and legal support", according to Gazmadh terms. She received them three times a week in her office to discuss and prepare the appeal. They had decided to follow her advice and to hire a lawyer to try to put all odds on their side. They had spoken to him by telephone. Once the appeal was submitted, a new stage of waiting started. Their social worker immediately warned them that they would not get a summons before 10 months or one year.

Time as constraint

Edona and Gazmadh met in the social services' office for Youth in the city of Korçë, where she worked as a receptionist and him as Section Chief of the governing party. She was 18 years old, him 23. A short time later, they got married. It happened two years before leaving Albania. At that time, they "worked a lot", but they also "went out a lot": meetings at friends, at parents, Gazmadh doing sport, she embroidered, as her mother did. Their life "was filled with activities", Edona says, when she evokes her past, to react against the monotonous daily life she was living in the shelter. "Since I am here, I have the impression that there are thirty hours in a day, and nevertheless I sleep a lot! [Laughs] Well, we do not have much to do (…) I do not go out a lot; I do not like going out, people look at me all the time. My husband goes to walk a little, but me, I do not do anything here. There is nothing to do. We get up late; we go to bed around midnight. We watch TV. We get up, I do the cleaning, and I cook. We speak, we fight, we watch TV or we listen to the radio, Chéri FM is very good. I go to the hospital or I stay here to read in French, they lent me some books. I do nothing, we have too much time here, we walk round and round, we are bored" (interview with Edona Bashe, shelter, 10/19/04). The Bashe spouses' lived their life between their room and the hospital, where Gazmadh took Edona for out-patient care twice a week9 . Sometimes, Gazmadh also made brief strolls in the shelter's neighborhood or stayed in front of the building's entrance, just the time to smoke two or three cigarettes. The daily life of people met in CADA is structured by the impression of "doing nothing" and "go round and round". The boredom about which Edona spoke reports a faintness caused by the dullness of the days out of a particular interest, that keep going again and again. This experience of a redundant temporality, of a time difficult to fill, reminds of the tramp's face described by [START_REF] Bauman | Le coût humain de la mondialisation[END_REF], which lives in the space, a heavy space, resistant, untouchable, which encloses time and shields it from the control of these people. At CADA, this space is, most of the time, made of the domestic environment. Watching TV, listening to the radio, doing the cleaning, sleeping, reading, discussing with the neighbors, seem to be the only available activities. They are perceived as ways to "spend" time and as the symptoms of that time which does not move. Many interlocutors expressed how they felt to live days with "thirty hours", as described by Edona, or as suggested by Gazmadh in the opening vignette, saying that "the watch was not moving forward". This "time reifying" language [START_REF] Gell | The anthropology of time[END_REF]) underlines someone's impression to find him suspended in an uncertain situation. As Elias mentions (1996Elias mentions ( [1984]]), time is often given certain properties of the processes' evolutionary aspects. Speaking about a watch that does not move forward is first of all reporting a stagnating situation that finds itself to the antipodes -it is, at least, the way Edona and Gazmadh often express it, but also many interlocutors -about life in the country, before asylum, before CADA, before waiting. From time to time, Edona and Gazmadh almost reluctantly participated in activities organized by the CADA entertaining team: visiting a museum, preparing cakes during a cooking session, going to the Floral park. Gazmadh found those "outings" childish, "we are not children!", he often repeated. The reason they participated was, above all, to fill that "empty" time. One afternoon, sat around the small table in their room, Gazmadh tells me about the feeling of "getting stuck": we are all the time here, we don't know what to do, days eternally last, always similar, we have too much time so far … When are we going to have a normal life? We are stuck, we cannot do anything, I smoke downstairs and that's all, we are locked up here, we are sometimes treated as children (conversation with Edona and Gazmadh, shelter, 11/2/04). The feeling of being "trapped" is shared by most of the interlocutors whom I met in CADA. It implies both a confinement in time -a present where one " does nothing" -and in spacea partially closed institution where the moves and visits are controlled, activities and daily routines are monitored, they sometimes feel to be treated childishly, as it leads to a loss, for the benefit of the institution, of the capacity of action and autonomy. That childishly experience sometimes motivated Gazmadh to convince his wife not to participate to the CADA entertaining activities. Many interlocutors used a prison's semantics to report their feeling to be "like in prison", "as prisoners", "behind bars". The impression of Gazmadh to be "trapped" well translates the waiting temporality and the spatial confinement: they are blocked in (and because of) the waiting, just like they are blocked in the shelter (because of the containment it induces). The above piece also reports the perception to be in a situation considered abnormal. The hope to have a "normal life" was often evoked by Edona and Gazmadh. We would like to have a house or an apartment, it is also good. Finish the treatment and be healthy. Stop with all this, have papers, find a work, for both. Have a stability, be busy, work as everybody, a normal life … And then have children (conversation with Edona Bashe, cafeteria of the Pompidou Centre, 1/27/05). The normalization for which Edona dreams depends on the material autonomy, the stability of a long-lasting legal status and the control of time. In other words, the waiting temporality also includes the hope of its end, of a "new life" with all that they did not have in their present life in CADA.

Accommodating to time

Ten months after her arrival to the shelter, Edona accepts an unexpected opportunity and begins to work off the books as cleaning lady. A young Russian woman living with her children on the same floor than the Bashe spouses, told her that she worked as a house keeper several times a week for a "French couple" the met thanks to the mother of one of her son's classmates. As she had to take care of her children, she could not work extra hours as she was offered, and suggested Edona to introduce her to a "couple of old French people". She encourages her to accept the job, telling her that it would allow her "to empty her head". "I do not like to do that, but, well, at least I would be doing something. I do not want to stay anymore in the room in front of TV, sleeping, it is not good for me, for my head. I do not like to clean the house; I prefer to cook and iron clothes. But it's good, it has made me busy for one month now, I go there three times a week, they are kind. I do not do it for money, yes, money is good for later, to rent an apartment, but I do not do it for that, I have to do something and, for the moment, I can only do the cleaning, then I do it" (interview with Edona Bashe, shelter, 2/23/05).

In spite of what is lived by Edona as a social downgrading, the most important thing for her is not much the salary she earns, but the impression of being useful and busy. One month earlier, Gazmadh had found an undeclared replacement on a construction site in a neighboring town to the CADA. He had worked during three weeks and that had made him "feel a lot better". After this first experience, he finds a dishwasher job in a Parisian bar where he works during four months. He is later hired as a construction worker. As the refugees living in humanitarian government camps, the asylum seekers I met often expressed feelings of powerlessness and uselessness, linked to the professional inactivity (Agier 2008: 207). Begin to work had just allowed Gazmadh and Edona to feel "active" and to somehow avoid dealing with time any longer. The money they earned is undoubtedly a motive to work on jobs they would never have imagined to do in Albania. To feel "less dependent" is also an important motivation, even more important, according to my interlocutors. For Edona and Gazmadh, working is a way "to do something" while waiting. Other asylum seekers also fit into the underground economy making their waiting time less boring -through the implementation of informal economic exchanges inside the shelter, as hairdressing salons and sewing workshops set up secretly in the rooms or selling cigarettes or perfumes in kitchens. Finally, for other asylum seekers, it is the associative voluntary work or the political activism that perform the same function. Although different, all these activities contribute to feel "less assisted" and to get back a positive feeling of oneself. They create obligations, allowing entering a temporality guided by specific constraints, printing a new rhythm in the days and an appearance of "normality". They finally open up the possibility of meeting people outside CADA, and existing in another way unrelated to the asylum claim. To be something else than an asylum seeker whose only activity is waiting. These activities can then be thought as tactics -in the sense of daily and tiny practices which take advantage of opportunities appearing at the moment (Certeau of 1980)that allow to by-pass the heavy effects of waiting by injecting a new texture into their present. "Getting out of the shelter for a moment, of all this, makes me feel good, to see other people, to take the bus to go to work, these things. I know we are not supposed to do it, well, we hurt nobody, and it is not theft. We really have no choice; it is to not become completely crazy!" (Conversation with Edona and Gazmadh, my apartment, in 3/29/05). Gazmadh is aware that his activity is illegal. In theory, within the transposition context of the European directive laying down minimal standards for the reception of asylum seekers 10 , the candidates for refugee status can request a temporary working permit before the Departmental Division of Labor, Employment and Professional training, if the French Office for the Protection of Refugees and Stateless Persons did not rule on their request after one year, or if they wait to be called in front of the judges who decide on the appeal. In this case, asylum seekers are subjected to the common legal rules applicable to immigrant workers for the delivery of a temporary working permit. The access to the employment market being firstly reserved for the French people, they will be authorized to hold a post only if, in the business sector and the geographical zone considered, the number of applications is not higher than the offer. Obtaining this permit is actually exceptional and, in most of the departments, the administration systematically refuses the right to work for asylum seekers, whatever the employment situation is (CNCDH 2006: 147). This practical employment prohibition produces a "field for illegal practices" (Foucault 1975: 285). Neither Edona nor Gazmadh had asked for an authorization like that. I have never met an asylum seeker in CADA who did it. So, concretely, in spite of the directive, the asylum seekers' reality did not change, they fit into the economic market in an informal way. While admitting that his activity was illegal, Gazmadh threw away the idea of being a thief and of people who "hurt" others. He justified himself by saying that he did not want "to become completely crazy", that he wanted to take care of himself. On April 15th, 2005, Edona and Gazmadh did not go to work. They were summoned to the Refugee Appeals Board "to defend their application for asylum". They are accompanied by a CADA social worker. Their lawyer is not there when they arrive. They unsuccessfully try to contact him to his cabinet and on his mobile phone. They had spoken during one hour with him three days ago, they had paid him the 850 Euros he had asked, "everything was ready". Finally, the session had to be postponed, due to the lawyer's absence. The next day, they will learn that he was sick. I believed that we were going to finish with that, that we were going to wait 21 days after which it was going to be over11 . Frankly, I was a little afraid this morning, I did not know how it would move, but that… How long are we going to wait to be summoned again? Still blocked with all this (conversation with Edona and Gazmadh Bashe, at a Coffee bar near the Refugee Appeals Board, 4/20/05). If working had helped them to kill the waiting time, the hearing postponing had reminded them that they were still depending on a decision and, therefore, "stuck in waiting".

Rethinking time

Sometimes concealed, occasionally almost tangible, the waiting time crosses the life of the men and women who seek asylum in France. It is also the fate of "tramps" [START_REF] Bauman | Le coût humain de la mondialisation[END_REF], "players" of globalization [START_REF] Bayart | Le gouvernement du monde. Une critique politique de la globalisation[END_REF], "poor people" [START_REF] Auyero | Patients of the State. An Ethographic Account of Poor People's Waiting[END_REF], "clandestines" [START_REF] Laacher | Le peuple des clandestins[END_REF]. Waiting, however, shapes every time in a different manner. In migrants' journeys, we can think of waiting as people lining up in front of a consulate to obtain a visa, as waiting for a smuggler or for better weather conditions to cross the border. Each waiting period has its non-written but well-established codes, its rhythms and spaces.

Edona and Gazmadh Bashe's practices and perceptions report various ways to make and conceive this imposed temporality, drawing three main sequences: -The temporal gap between the submission of the asylum application and its outcome appears first, as an opportunity, as it introduces a break in CADA and the possibility of reconstructing oneself after a circulation and wandering trajectory.

-Waiting time is lived as a constraint which manifests by a retreat, a sense of emptiness which is added to a sensation of uncertainty. Uncertainty related to the result of the application and for projects in the future. On this stressful daily life, it is often also inevitable to think about the suffering of a past of violence which caused the decision to exile.

-Waiting time is by-passed by doing activities outside the shelter -in this particular case, working -which imply new temporal frames, new networking, new spaces. These sequences must not be thought as a uniform and linear chronology. They are, on one hand, punctuated by the phases of the asylum procedure and, on the other hand, there may be comings and goings in the temporal stages, thus moving from a period where waiting is hidden under other temporal constraints, to another one where it comes back and is translated by the confinement in the shelter. It is in these moments of boredom that the double dependence -institutional and economic -of candidates for refugee status, established by the ban de facto to work, is felt most deeply. Sometimes waiting was not only due to the asylum claim, but also to the waiting of the news from the parents with whom contact was lost, the waiting of a political change in the country of origin, or the hope of a "new life". To wait and to hope were then both articulated in the same temporality 12 . In Edona and Gazmadh Bashe's experience, waiting appears at the same time as a break in their trajectory, which they perceive as an unsettled putting, and as a continuity as they sometimes experience a stretching temporality which seems permanent. If waiting experiences of poor people subjected to the Ministry of Social Development' decisions in Argentina « persuade the destitute of the need to be patient, thus conveying the implicit state request to be compliant clients » (Auyero 2011: XXX), thus associating the waiting with a disciplinary dimension (see Schwartz 1975: 189), those of the asylum seekers met in reception centers in France rather bring together waiting and confinement. The normalized waiting is here aggravated by the particular life conditions in CADAassistance and control, support and vigilance, protection and childishly acting -where people who only share the experience of asylum seeking live. This alienation of time is more an effect of the bureaucratic practices than a political objective, but it certainly is a way to test the administration. Waiting "durably changes", that is to say, during all the time that the expectative lasts, the behavior of the person being, as we say, suspended to the awaited decision" (Bourdieu 1997: 270).

The public hospitality offered in CADA entails a close relationship between time, space, and the exercising of power. As with most of the interlocutors I met during my fieldwork, Edona and Gazmadh Bashe experienced a contraction of space and an expansion of time. The waiting of asylum seekers can be understood both as a form of government and as a daily (social and relational) activity that involves many practices engaged in so as to pass time. Contrary to what seems to be suggested by often-used expressions such as "it is an empty time" or "it is a complete void", waiting is not in fact absence. Rather, it is populated by a multitude of everyday activities that contribute to filling it. It is through these activitiesfrom the most ordinary and trivial to the more inventivethat the possibility of freeing oneself (at least partially) from the imposed temporality is likely to emerge. In other terms, it is in this capacity to find ways of coping with the waiting process that the possibility of agency lies. It is about the possibility of (once again, at least partially) choosing, deciding, in a present characterized by uncertainty and doubt. *** Edona and Gazmadh Bashe will wait a year for the new summons to the Refugee Appeals Board. Anxiety fills in the three weeks that follow the hearing. The waiting ends up when they have the result of their appeal. They are dismissed. They have four weeks to leave the CADA. Last time I heard from them, two years later, they were still in irregular situation and shared an apartment with two other couples near Lyon, she did the cleaning in private homes, he worked on a construction site. They were expecting a baby.

To preserve my interlocutors´ anonymity and to keep their comments confidential, names and dates have been modified.

At the time Edona and Gazmadh Bashe asked for asylum, law n° 2003-1176 of December 10, 2003 layed down the Geneva Convention's conditions for application and the granting of protection as conventional

Since 2009, the Refugees Appeals Board became the French Court of Asylum (Cour nationale du droit d'asile).

This was highlighted in a report written by the General Inspectorates of Finances, Social Affairs and Administration in April 2013. It strengthens a statistical study conducted in almost sixty CADA by the France terre d'asile NGO at the time of my fieldwork. That study revealed that the average rate of the recognition of a

Edona sometimes mentioned her husband's patience and support, « another would have divorced with a wife like this », she told me once, pointing her injured faced.

August 23, 2005August 23, decree (n˚ 2005August 23, -1051)).

Following the convening to the French Court of Asylum (previously the Refugee Appeals Board), the waiting time has a clear duration, as the decision is posted on the lobby of the Court's building exactly three weeks after the hearing.

The Spanish language is here very explicit because esperar means both to wait and to hope. This double meaning can be found in the etymology of the French word attendre which takes to the latin tendere, meaning « lay our spirit toward. » The focus here is on the dimension of hope and expectative held by waiting. This dimension can be found in the French Academy dictionary, edition of 1762 where the verb to hope appears within the acceptations of waiting.