T Kozuka
email: kozka@kumamoto-u.ac.jp

H Honda

S Fukuda

M Kawahara

The Effect of Magnetic Field on Metal Anodizing Behaviour

Keywords: metal anodization, magnetic field imposition, bio-materials

Metal anodizing process has been utilized in various surface treatments. In the field of biomaterials, in order to improve biocompatibility with biological tissue, metal anodizing of titanium or zirconium has been adopted. In the former work with imposition of intense electric field, it is found that the electric field increases the anodizing reaction rate, and the suitable range of anodizing voltage for obtaining preferable surface morphology becomes wider. On the other hand, magnetic field can promote the metal substitution reaction and it also increase the metal anodizing. Furthermore, magnetic field has the possibility of ordering the pore arrangement in the anodized film. Metal anodizing experiments using phosphoric acid solution is conducted under parallel and vertical magnetic field imposition up to 1T. It is found that magnetic field can promote the anodizing reaction and pore formation. On the other hand, vertical magnetic field can promote the anodizing reaction heterogeneously in relatively low voltage. For high voltage of 300V, the pore morphology ware almost same for the cases of without magnetic field, parallel magnetic field imposition and vertical magnetic field imposition, but the shape and the size becomes uniform in the case of magnetic field imposition. Magnetic field is effective not only the promotion of the anodizing reaction but also the homogenization of pore formation due to MHD and micro MHD effect.

Introduction

In the field of biomaterials, titanium or zirconium alloys are mainly used because of their good biocompatibility and Young's modulus close to the bone tissue. In order to increase the performance of biomaterials, metal anodizing has been conventionally adopted as a surface treatment, where the anodized oxide film can be divided into two morphologys. One is microscopic honeycomb structure under lelatively low anodizing voltage, and the other is porous structure due to dielectric breakdown phenomena under high anodizing voltage. From a biocompatibility standpoint, porous anodized film more preferable, and the size and regularity of pore arrangement are strongly releted with the biocompatibility. Many researchs has been done with various anodized voltage and the electrolytes [1].

In this study, the effect of magnetic field imposition on the morphology of anodized oxide film is investigated using superconducting magnet. In former work, it is found that an electric field imposition has some influence on the critical anodizing voltage for dielectric breakdown and the regularity of pore arrangement in the anodizied film [START_REF] Kozuka | 7 th Int. Conference on Electromagnetic Processing of Materials[END_REF]. On the other hand, in the condition of magnetic field imposition, MHD effect or micro MHD effect can be expected as the same way in electro-deposition behavior of cathode electrode [3][4]. In this paper, basic phenomena of metal oxidation and pore formation in the anodized film on Ti plate will be revealed from the experiments of metal anodization from pphosphoric acid with the anodized voltage up to 300V. Furthermore in order to clarufy the effct of magnetic field imposition, Ti anodizing experiments will be conducted where the anodizing cell will set in the bore of superconducting magnet. The properties of anodized film will be investigated using XRD and SEM.

Experiments

In the preparation of anode plate, a titanium plate is polished with silicon carbide and diamond paste and cleaned with an ultrasonic device. Metal anodizing of Ti plate is conducted in potentiostatic mode with the electrolyte of 1.0 mol/L phosphoric acid and various anodizing voltage up to 300V. Fig. 1 shows the schematic drawing of an experimental cell in the magnet bore in the case of (a) parallel magnetic field and (b) vertical magnetic field. The strength of magnetic field is up to 1T. The reactions on the both electrode surfaces are considered to be ;

Cathode : 2H 2 O + 2e -→ H 2 + 2OH - (1)
Anode :

4OH -→ H 2 O + O 2 + 4e - Ti + O 2 → TiO 2 (2)
Actual anodic reaction is very complicated including ionization and discharge. And in the range of over the critical voltage for dielectric breakdown where many pores appears in the oxide film with micro arc causing to heat generation.

Anodized oxide film around the pore melted by the heat and it is precipitated again around the pore resulting smooth pores. That is considered to be advantageous for the biocompatibility. In order to ascertain the pore formation and pore arrangement, surface oberbation is conducted using SEM. Furthermore, thin film XRD measurements is conducted to examine the oxide formation on the anode plate.

Results and Discussion

In the range of under the critical voltage for dielectric breakdown, the surface morphology becomes bumpy by imposing magnetic field with many submicron pores. And the uniformity of the pore size and arrangement is better in the case of parallel magnetic field than that in vertical magnetic field as shown in Fig, 2. In the parallel magnetic field, anodizing electric current is perpendicular to magnetic field, so that the strong convection appears in the vicinity of anode surface. This MHD effect can promote the oxidation reaction due to the increase of mass transfer. In the vertical magnetic field, MHD effect can not be expected, but micro MHD effect can promote the oxidation reaction which is not so strong under 1T magnetic field. In the relatively high anodizing voltage of 150V-250V, dielectric breakdown occurs in the same way regardless of the imposition of magnetic field, but magnetic field affects the pore size and pore arrangement. Fig. 3 shows the surface morphology of 200V anodizing voltage without magnetic field and with parallel or vertical magnetic field. The black spots indicate the pores caused by dielectric breakdown, and the pore size increase by imposing magnetic field. In the parallel magnetic field, it seems that the surface is completely covered by oxide in the same way without magnetic field, but the oxide layer becomes thicker. In the vertical magnetic field, pore formation occurs heterogeneously and each pore becomes larger than that with parallel magnetic field. Fig. 4 shows the XRD pattern of anodized film. Because the anodized film is very thin, metallic Ti peaks appears in all patterns. In the case of parallel magnetic field, the peak of TiO 2 is highest, so that the oxidation reaction strongly promoted by MHD effect as shown in Fig. 3 (b). In the case of vertical magnetic field, many peaks of Ti indicate the non-uniformity of pore formation as shown Fig. 2 (c). In this situation it seems that another mechanism control the pore formation. The electrical conductivity of oxide film is very small, the pore formation should result the non-uniformity of electric current in the vicinity of the anodizing surface. Under the imposition of magnetic field of 1T, the Lorentz force due to the interaction of imposed magnetic field with the transverse electric current. This Lorentz force causes to small vortex flow corresponding with each pore. Mass transfer can be promoted by this vortex flow for a relative large pore. On the other hand, small pore formation is suppressed by this vortex flow. That is the reason of the non-uniformity of large pore as shown in Fig. 4 (c).

In relatively high voltage of 300V, pore size and pore arrangement is almost same regardless of magnetic field imposition as shown in Fig. 5. However, the anodized surface becomes smooth and the regularity of pore arrangement increase in the case of vertical magnetic field as shown Fig. 5 (c).

Conclusion

In order to understand the metal oxidation and pore formation phenomena in a metal anodizing process aiming to improve the biocompatibility of titanium or zirconium alloys, some Ti plate anodizing experiments using phosphoric acid electrolyte is conducted. And then, effect of magnetic field imposition on the anodizing behavior is examined. The obtained results can be summarized as follows.

-In the range of anodizing voltage before dielectric breakdown, i.e. under the critical breakdown voltage for Ti plate, imposed magnetic field can promote the anodizing reaction and make the surface microscopic bumpy morphology. -In the range of anodizing voltage over 150V, dielectric breakdown occurs in the same way regardless of magnetic field imposition. And parallel magnetic field can promote the surface oxidation reaction and pore formation uniformly because of MHD effect, but under a vertical magnetic field, pore formation and oxidation reaction becomes heterogeneous. -In relatively high voltage, pore size and distribution is almost same regardless of magnetic field imposition. However, the anodized surface becomes smooth and the regularity of pore arrangement increase in the case of vertical magnetic field.

Fig. 1 :

 1 Fig.1 : Schematic of metal anodizing cell in the magnet bore.

Fig. 2 :

 2 Fig.2 : SEM images of the anodized surface with the anodized voltage of 100V.

Fig. 3 :Fig. 4 :

 34 Fig.3 : SEM images of the anodized surface with the anodized voltage of 200V.

  Fig.5 : SEM images of the anodized surface with the anodized voltage of 300V.


Yannick Bourrier
email: yannick.bourrier@lip6.fr

Francis Jambon
email: francis.jambon@imag.fr

Catherine Garbay
email: catherine.garbay@imag.fr

Vanda Luengo
email: vanda.luengo@lip6.fr

An Interaction Centred Approach to the teaching of Non-technical Skills in a Virtual Environment

Keywords: Ill-Defined Domains, Non-Technical Skills, Critical Situations, Virtual Reality Environment

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

In most domains involving expert knowledge, there is a number of cognitive and social factors influencing human performance, which are commonly described as Non-Technical Skills (NTS). In this paper, we aim to showcase the challenges which arrive from the learning of NTS inside a Virtual Environment (VE), and to discuss the potential and limitations of a number of approaches recently used in this domain, in the light of an ill-defined perspective, and under the scope of their application to the domains of driving and medical surgery, two domains where we have access to high quality virtual environments.

What are NTS? They range from purely social skills such as communication, team working and leadership, to cognitive skills such as decision making and situation awareness, and personal resources such as stress and fatigue management. They have been extensively studied in medical surgery [START_REF] Flin | Development of the NOTECHS (non-technical skills) system for assessing pilots' CRM skills[END_REF][START_REF] Flin | Identifying and training non-technical skills for teams in acute medicine[END_REF], and some have been studied also in relation to driving [START_REF] Gugerty | Situation awareness during driving: Explicit and implicit knowledge in dynamic spatial memory[END_REF][START_REF] Ma | Situation awareness and workload in driving while using adaptive cruise control and a cell phone[END_REF][START_REF] Recarte | Mental workload while driving: effects on visual search, discrimination, and decision making[END_REF]. In these two domains, it has been demonstrated that NTS have an influence, positive or not, on technical skills (TS). Such an influence may be even more important in critical situations, i.e. unique events of variable severity which are hard to anticipate [START_REF] Merrill | Constructivism and Instructional Design[END_REF]. For example, an unexpected complication during a medical intervention might fall out of the area of expertise of a practitioner, which would require him to firstly, identify his own inability to provide a correct technical response to said situation (situation awareness), and secondly, to decide to ask for help to someone else (decision making). If the patient's health is deteriorating quickly, such a demand might be done under stressful conditions (stress management), which could in turn influence our first practitioner's ability to clearly transmit a diagnostic of the situation (communication). Poor stress management and communication skills from our first practitioner may result in a diagnostic error and a third party committing a technical mistake. Moreover, all of these effects are highlighted in visual-gestural activities which are seen in driving or surgery. Due to their physiological anchoring, they are particularly difficult to formalize.

We discuss in the paper the advantages of using a combined enactive and situated learning approach to this problematic. Virtual Environments (VE) appear appropriate in this perspective. They offer the possibility to immerse the apprentice in situations whose parameters may be controlled from the outside, while mastering the situation's degree of criticality. They also provide facilities with regards to the monitoring of human behaviour thanks to the numerous ways to gather traces of interactions from the learner with the virtual environment, such as actions on simulation controls or perceptions of information emanating from the virtual world. Most VE however, seem to put the main focus on the realism of a simulation, sometimes at the expense of computer assisted teaching capabilities.

Teaching NTS therefore raises a number of research questions related to the construction of an intelligent learning environment, which may be approached under the ill-defined problem perspective, as identified by Lynch et al. [START_REF] Lynch | Defining Ill-Defined Domains; A literature survey[END_REF]. Firstly, while domains of technical activities such as driving or some very procedural aspects of medical surgery are well-defined, there is no formal theory of what is a correct NTS display in response to a critical situation, nor there is a formal theory of how to teach NTS. Secondly, we expect some of the previously mentioned NTS to have high variations among individuals. For example, a situation which is stressful for someone might not be for another, depending on both participants' technical ability as well as the inter-individual differences to stress response between humans. A system evaluating one's ability to cope with stress will have to take into account these variations in order to provide new relevant learning situations. Finally, given that NTS are essentially "behavioural markers that contribute to superior or substandard performance within a work environment" [START_REF] Flin | Development of the NOTECHS (non-technical skills) system for assessing pilots' CRM skills[END_REF], they can be perceived as factors which influence how efficiently TS are executed. We ask that such an influence is reciprocal, and that failure to provide a correct technical response to a critical situation will also influence a participant's non-technical behaviour. The co-dependency between NTS and TS in domains involving technical activity is at the centre of our problem. This falls close to the notion of overlapping subproblems as described by [START_REF] Lynch | Defining Ill-Defined Domains; A literature survey[END_REF], where a task cannot be separated into a continuation of independent sub-problems. However, in the case of NTS evaluation in critical situations, not only are the sub-problems overlapping, the very skills we seek to diagnose overlap as the borders between technical and non-technical expertise can be diffuse.

In this paper, we focus on how to design intelligent learning environment assisted teaching of technical and non-technical skills during critical situations, inside of a virtual environment, and applied to driving and medical surgery. In the next section, we will review more precisely the links between NTS and TS in these two domains according to studies in applied ergonomics and cognitive psychology. Then, we will highlight the benefits related to the teaching of these skills inside a VE, as well as the limitations of such a teaching with regards to current approaches to learning in VE. Finally, we will present approaches which have been used in Intelligent Tutoring Systems (ITS) in order to enable learning in domains presenting similar ill-defined problems. Based on this analysis, we explore some further elements characterizing our domain under the ill-defined perspective and discuss some of the corresponding designing issues.

Context

Non-technical skills in driving and medical environments

NTS can be defined as "the cognitive, social, and personal resource skills that complement technical skills, and contribute to safe and efficient task performance" [START_REF] Flin | Safety at the sharp end: a guide to non-technical skills[END_REF]. They have an influence on the worker's TS and include situation awareness, decisionmaking, teamwork, leadership, stress and fatigue management, which can either increase or decrease the risks of worker error.

The teaching of NTS has been explored in lengths within the medical domain. Because of the importance these skills have in operating theatres, psychologists have made attempts to evaluate the non-technical proficiency of surgeons, anaesthetists and nurses. These attempts resulted in rating systems such as ANTS [START_REF] Flin | Anaesthetists' non-technical skills[END_REF], or NOTSS [START_REF] Yule | Surgeons' non-technical skills in the operating room: reliability testing of the NOTSS behavior rating system[END_REF] where NTS used by medical practitioners were identified from cognitive task analysis, and then decomposed in a series of behavioural markers. With regards to driving, NTS also play an important role and attempts have been made to evaluate some NTS in the handling of a risky situation [START_REF] Hatakka | From control of the vehicle to personal self-control: broadening the perspectives to driver education[END_REF][START_REF] Underwood | On-road behaviour of younger and older novices during the first six months of Driving[END_REF]. NTS evaluation is therefore often achieved from the observation and the rating of behavioural markers by other experts. While this method can result in a fine evaluation of some NTS [START_REF] Flin | Development of the NOTECHS (non-technical skills) system for assessing pilots' CRM skills[END_REF], others, like stress or fatigue management, are difficult to detect this way [START_REF] Flin | Anaesthetists' non-technical skills[END_REF]. However, because they influence technical resources in both domains, their influence should be noticeable in a variation of a participant's TS. Therefore, the means of evaluating a participant's NTS can be found both in their behaviour and also in the variation of their TS.

NTS are often studied under the scope of critical situations. According to Merril [START_REF] Merrill | Constructivism and Instructional Design[END_REF], these situations are unique, with an inconstant degree of gravity making them hard to anticipate. They also are at the origin of a lot of mistakes, especially in the operating theatre [START_REF] Yule | Non-technical skills for surgeons in the operating room: a review of the literature[END_REF]. Critical situations are strongly related to NTS, firstly because a failure to correctly apply a NTS may result in a situation becoming critical [START_REF] Flin | Anaesthetists' non-technical skills[END_REF], and secondly, because when a situation is critical, there is a higher propensity at non-technical failure [START_REF] Fletcher | Anaesthetists' Non-Technical Skills (ANTS): evaluation of a behavioural marker system †[END_REF]. We should also note that a situation which may be critical to one person might not be for another, rather, the degree of criticality can vary strongly among individuals. For example, someone who has already been confronted to a situation involving a particular risk will be more likely to understand how this situation should be treated, than someone who encounters it for the first time.

The use of virtual environments (VE) for learning

Virtual environments for learning have known a growing interest in the last years. Among the features that characterize their design and use, we can cite the possibility to immerse the trainee in a physical environment in which his or her visual-gestural behaviour may be monitored under formalized scenarios [START_REF] Dillenbourg | Virtual learning environments. 3rd Hellenic Conference" Information & Communication Technologies in Education[END_REF]. This immersion is key to the involvement of the NTS that we are interested in pursuing. Furthermore, Pearson and McLafferty [START_REF] Pearson | The use of simulation as a learning approach to non-technical skills awareness in final year student nurses[END_REF] state that "the use of simulation as an educational strategy of active learning allows the students to develop, refine, and apply their knowledge within a safe environment". This is particularly pertinent in critical situations which may have grave consequences in the case of error, not only in the medical domain [START_REF] Flin | Identifying and training non-technical skills for teams in acute medicine[END_REF] but also in driving, where unforeseen events can result in accidents. The evaluation of NTS in medicine has always been done in simulated environments, either in the real world [START_REF] Fletcher | Anaesthetists' Non-Technical Skills (ANTS): evaluation of a behavioural marker system †[END_REF] through the use of role play, or through the use of VE [START_REF] Sleeper | The use of hi fidelity simulation to enhance nursing students' therapeutic communication skills[END_REF]. For driving, skills such as Situation Awareness or Decision Making skills were detected through the means of computer based simulations [START_REF] Gugerty | Situation awareness during driving: Explicit and implicit knowledge in dynamic spatial memory[END_REF] or controlled instrumented cars [START_REF] Recarte | Mental workload while driving: effects on visual search, discrimination, and decision making[END_REF].

Real life simulations are often carefully planned from the start. Therefore, all of the situation's parameters are under control which can simplify process of NTS evaluation (the experts know which elements to consider) however, such a planning requires a lot of preliminary work in order to prepare the scenario, and while the evaluation itself is indeed simplified, this task restrains the possible number of critical situations which can be proposed to the learner. Real-life simulations become one off exercises, with little reusability. This approach therefore has a number of downsides, especially with regards to the learning strategy related to the teaching of NTS: in most cases, training is the result of NTS evaluation and a post-simulation debriefing. Overall, at least in the medical domain, such a training resembles more as a series of attempts at raising awareness at the importance of NTS in critical situations rather than teaching skills which may be gradually improved by the learners. In order to provide a larger number of learning situations, the use of VEs strikes us as appropriate, as the possibility to manipulate every element inside a virtual world can provide higher resources availability [START_REF] Burkhardt | La réalité virtuelle pour l'apprentissage humain[END_REF]. In other words, VEs can potentially generate an important number of critical situations inside of which NTS can be tested, allowing the construction of a true strategy for the learning of NTS. Because VE's create a safe learning environment and can provide multiple unique critical situations for the learning of NTS, they can strongly contribute to the successful training of these skills. Our objective is to provide an efficient VE for the training in NTS in different domains by targeting the critical situations which are the more adapted to the specificities of each learner, given a number of constraints such as the duration of a training session (about 1 hour) and the limited number of training sessions for a learner. In the next session, we will first present a number of interaction-based approaches to teaching in VE, then explain why the learning of NTS inside a VE needs to take into account the differences among learners, and why it is necessary to model the learner's knowledge in order to maximise the efficiency of the learning experience. What is of interest is the kind of coupling that may be achieved between the learner's skills and behaviour and the scenarios played by the virtual environments. As we will discuss in the following paragraphs, this coupling leads to ill-defined issues that are particularly interesting to consider in the VE context.

Modelling the interaction between learner and VE

The existence of the aforementioned links between NTS and critical situations underlie the necessity to place the interaction between learner and VE at the centre of our approach, in order to provide the most relevant situations for the learning of NTS. There are different approaches to learning which put the interaction of an individual with the world at its centre, two of them being the enactive approach to learning and the constructivist-based situated learning. In this section, we will present both of these approaches with their benefits and downsides, and explain why it is necessary to have a modelling of the learner's knowledge in order to teach NTS.

The enactive approach

A first approach to this representation can be found in the principle of enaction [START_REF] Varela | L'inscription corporelle de l'esprit in Paris[END_REF]. When transposed to Virtual Reality, an enactive system is a system constructing a world, while being constructed by it [START_REF] Varela | L'inscription corporelle de l'esprit in Paris[END_REF]. In this view, the coupling between the VE and the user is intrinsic as an individual's actions will result in a modification of the world by the system, and vice versa. Knowledge therefore becomes the result of this interaction between individual and world, and can be found in the perceptions and actions traces that this interaction creates. Given that the system evaluates learning as the result of the interactions between an individual and the virtual world, in this approach knowledge is purely empirical, and can therefore be evaluated from a phenomenological perspective. The focus is put on what the learner experiences directly, and knowledge can be seen as either structural (i.e. describing the properties of the world), factual (i.e. describing the current state of the world) or case-based (i.e. describing a number of correct decisions when confronted with a situation) [START_REF] Fricoteaux | Interaction informée par un système décisionnel pour un retour multimodal en environnement virtuel: application à la formation au transport fluvial[END_REF].

The main benefit of this approach, when it comes to the teaching of NTS, can be seen in this phenomenological perspective to learning. Since knowledge is the result of empirical experience, learning becomes highly specific to an individual. Considering the nature of the skills we aim at teaching, the ability to take into account individual differences for the learning of NTS is crucial and therefore this interaction-centred approach is appropriate in that matter. Moreover, in order to be efficient, the enactive approach has to put the credibility of the virtual world in its centre [START_REF] Thouvenin | Interaction et connaissance: construction d'une expérience dans le monde virtuel[END_REF]. Because knowledge is the embodied consequence of the perceptions and the actions of an individual on a world, said world (in our case the enactive VE) has to be able to react and modify itself according to the learner's actions so that learning takes place. Therefore, and because of this focus, enactive VE are deemed as appropriate in our case where the learner is confronted with critical situations that he or she will have to address, and whose consequences will highly differ based on his or her actions. However, while there are benefits in terms of learner modelling, downsides exist when it comes to the teaching of NTS as a whole. The fact that we target empirical knowledge rather than a specific skill may result in a loss of efficiency when it comes to selecting a new learning situation. For example, an enactive system may evaluate a learner's behaviour in a certain situation with a degree of validity, and propose a new situation based on this evaluation, but it will not try to identify the specific NTS which was deficient. Therefore, the choice of a new learning situation might lack some degree of precision when it comes to targeting the skills that really need to be improved for a learner. Being able to assess which NTS in particular should be improved could greatly increase training effectiveness. This constraint is even stronger in our domain where we plan to teach NTS in driving and medicine in VE's, and therefore are subject to the time constraints of the training sessions. Because a session only lasts one hour, being able to select more accurately the most important skill to target for a given individual is very important. Some modelling of the learner's knowledge to ascertain which skill needs to be focused upon is therefore needed.

Situated learning and the constructivist approach

Another approach to the modelling of the interaction between a learner and a VE can be found in an extension of the constructivist view to learning initially proposed by Piaget [START_REF] Piaget | The origins of intelligence in children[END_REF]. According to Piaget, learning originates from the interaction between a learner and the world and "should be situated in realistic settings and testing integrated with tasks, not treated as a separate activity" [START_REF] Woolf | Building intelligent tutoring systems[END_REF]. However, in this view and more precisely in one of its expansions, namely the situated learning approach, the type of knowledge is central to learning [START_REF] Luengo | Take into account knowledge constraints for TEL environments design in medical education[END_REF]. While enaction, constructivism and situated learning share the notion of interaction as being central to the emergence of knowledge, the latter argues that different types of teaching should be applied to different natures of knowledge.

Applied to VE's, situated learning approaches often come with an important background work in order to understand the knowledge underpinnings characterizing a domain. A task is evaluated, not only in the representation of the interactions between VE and learner, but also in the specific knowledges involved in each of the learner's actions or strategies [START_REF] Luengo | Take into account knowledge constraints for TEL environments design in medical education[END_REF]. Knowledge being de facto represented for a learner, targeting specific elements of the domain become possible. For example, in TELEOS [START_REF] Luengo | Take into account knowledge constraints for TEL environments design in medical education[END_REF], an ITS for the learning of orthopaedic surgery built within a situated learning paradigm, the distinction is done between the types of knowledges. The type of the feedback will change whether it is an empirical or a declarative aspect which is targeted.

The benefits of this approach are seen in this understanding of which type of knowledge is actually being mobilized by the learner. Because we have deconstructed the learner's actions in the world as a result of certain skills being used, we can target with more precision the ones which might be deficient. This seems especially appropriate in our problematic of NTS and TS learning in virtual environments. Some NTS and most of the TS in the medical and driving domains can be noticeable through cognitive task analysis. Therefore, they may also be identifiable in a VE through a careful decomposition of these skills in terms of knowledge types. In this respect, the situated learning approach is interesting, because a precise evaluation of these skills can help the system determine which ones need to be improved for a given learner.

Drawbacks come from the lack of a clear pedagogic strategy which translates in a deficit of efficiency when it comes to integrating the training in a learning curve. Because the focus on the type of knowledge is so strong, feedback only takes place outside of the virtual world, and will be less connected to the actual learning environment. In situated learning applied to virtual environments, the interaction between learner and system is important, but may sometimes be overshadowed by knowledge of the domain itself. Given the specificities of NTS and their links to situations which are by essence unique, we argue that they should be best taught by the empirical experience of a large number of critical situations. While knowledge of the domain is key to know which skill should be targeted for a given learner, we hypothesize that the teaching of NTS should be done by a succession of empirical experiences, and not through post simulation feedback.

Exploring criticality through the construction of knowledge

We saw earlier the interests of adopting an enactive approach for the teaching of NTS in VE. According to this approach, learning is the embodied consequence of an individual's interaction within the world in which he or she evolves. In our case, this means that the NTS will be learned by a succession of confrontations between the learner and critical situations, under the assistance of immersive teaching methods. This is a logical conclusion because NTS are non-procedural by nature, rather, they appear to cope specifically with the lack of an adapted procedure to deal with a given situation [START_REF] Marchand | Les retours d'expériences dans la gestion de situations critiques[END_REF]. For all these reasons, our approach should first of all be underpinned in the principles of enaction applied to VE. However, it should still be necessary to adopt some aspects of situated learning, more precisely, the modelling of knowledge, in order to reach a higher training efficiency. Critical situations are by nature challenging, and some challenges may simply be too hard for a learner given a certain degree of technical and non-technical expertise. On the opposite side, a situation which would be deemed as critical for someone will not be for another person who may have already been confronted to a similar situation. A situation may therefore be critical for an individual and not for another, depending on their TS level and the way they can handle the non-technical aspects related to it. For example, a patient in mortal danger needs to be treated according to a technical procedure known by the surgeon. Such a situation will be more or less critical depending on the nature of the practitioner. A surgeon with an average stress management ability will find it more difficulti.e. criticalthan one with a high score of stress management. Therefore, in order to provide efficient NTS training, it is necessary to target situations which have the right degree of criticality for a specific individual. If the degree is too low, the situation will not be critical and therefore NTS will not be mobilized. But if the degree is too high, the situation will simply be too difficult and a failure can have a very negative impact for the learner. Providing the right degree of criticality is crucial to the good teaching of NTS, therefore, some form of knowledge modelling is in our case, necessary.

We orient ourselves in the direction of an enactive VE including a degree of learner's knowledge modelling. In other words, we aim at evaluating the learner's performance in terms of TS and NTS inside a critical situation, while respecting the principles of enaction in order to maintain the necessary degree of realism for the simulation. The evaluation of a learner's skill level when confronted with a given problem has been explored at lengths in the ITS literature, let us explore the difficulties such a knowledge modelling problems poses in an interaction-centred VE such as ours. Fig. 1. In order to teach NTS in a virtual world, the system will be fed with a number of data corresponding to a learner's behaviour. Theses traces lead to the evaluation of the learner's TS and NTS level. From this diagnostic, a new learning situation can be selected and then played which will result in new traces being produced and a new evaluation process being done.

Teaching non-technical skills inside of a virtual world: issues from an ill-defined perspective

In 2006, Lynch et al. [START_REF] Lynch | Defining Ill-Defined Domains; A literature survey[END_REF] attempted to cover the different aspects which made a teaching problem ill-defined in an ITS Framework. Following this breaking down, researchers argued that knowing which aspects of a problem were ill-defined could provide insights for the choosing of the more appropriate modelling technique [START_REF] Fournier-Viger | Building intelligent tutoring systems for ill-defined domains[END_REF], and started questioning whether an ill-defined teaching problem should be divided in the two notions of domain and task [START_REF] Mitrovic | Revisiting Ill-Definedness and the Consequences for ITSs[END_REF]. Fournier-Viger et al. [START_REF] Fournier-Viger | Building intelligent tutoring systems for ill-defined domains[END_REF] suggested that because the main focus of an ITS was to provide the learner support to individual tasks, the notion of domain might be unnecessary. Looking at the problem of NTS teaching inside a virtual world, this distinction appears useful in order to illustrate the specificities of our twofold approach. Situated learning aims at representing the specificities of the knowledge we seek to teach and as such raises research questions which are purely related to the domain, while the enactive approach may represent the interaction-centred challenges related to the learner's realization of a given task. In this session, we take a look at the modelling of NTS inside of a virtual world from the perspective of both the domain and the task, following [START_REF] Lynch | Defining Ill-Defined Domains; A literature survey[END_REF]'s definition of what characterizes an illdefined problem. We also point out some further aspects that have not been encompassed yet in the ill-defined problems literature.

5.1

The ill-defined problems related to situated learning and knowledge modelling.

When it comes to modelling learner's knowledge, one of the main criteria characterizing ill-defined domains is the absence of a complete formal theory of the domain.

Here we actually aim at evaluating two different domains, which are technical and nontechnical skills in driving or medical surgery. Taken separately, are these two-domains ill-defined? Is technical expertise ill-defined? A technical gesture, whether it is in driving or in medical surgery, is partly declarative, partly procedural and partly empirical; in other words, it corresponds to the good choice of a given procedure preferentially to another, and the good implementation of such a procedure. While some aspects related to the evaluation of a TS in a VE may well be ill-defined, the description of a technical gesture in itself is almost always known and clearly defined. For example, in driving, hill start in a manual car can be described as: (1) lift the handbrake, (2) disengage, (3) pull-away slowly while handing down the handbrake. Theoretically, it is a succession of gestures produced in a certain order. Therefore, TS in themselves seem to have a degree of formal theory.

Is there a domain theory of NTS? Cognitive skills such as situation awareness and decision making, and social skills such as team working have been identified through the means of cognitive task analysis, when evaluated in real-life simulations in the medical domain [START_REF] Flin | Development of the NOTECHS (non-technical skills) system for assessing pilots' CRM skills[END_REF][START_REF] Yule | Surgeons' non-technical skills in the operating room: reliability testing of the NOTSS behavior rating system[END_REF]. If such an analysis is possible, then these skills should be well-defined theoretically. Other NTS such as stress management for example, have been defined by psychologists or work specialists. From the early work of Lazarus in 1966 [START_REF] Lazarus | Psychological stress and the coping process[END_REF], the effect of emotion on behaviour has been studied in depth. A cognitive-motivational-relational theory of emotion has been proposed, emphasizing in particular the mediating processes (cognitive appraisals of situational demands and personal coping efforts) that affect the relationship between a person and its environment.

In themselves, both technical and non-technical skills have a degree of formal theory. The definition varies in function of the technical domain, but it is certainly more defined than the more exploratory aspects of astrophysics for instance, one of the examples proposed by [START_REF] Lynch | Defining Ill-Defined Domains; A literature survey[END_REF] in order to illustrate domains without a formal theory. We argue that our domain, though, is still ill-defined knowledge-wise from a perspective that has not been covered by [START_REF] Lynch | Defining Ill-Defined Domains; A literature survey[END_REF]'s definition, because technical and non-technical skills are involved in a single perceptual-gestural activity. Even if both aspects are partially illdefined in themselves, the central difficulty can be found in that they appear in the same gestures; therefore, evaluation-wise, technical and non-technical abilities overlap. We face here a case where two different domains overlap and can only be observed together. Taken separately, they are well-defined. Put together, they become ill-defined as the ties between them are diffuse and can change from one individual to another. We ask that this is a new form of problem not yet identified by previous approaches to illdefined domains, and which should be encountered whenever the goal is the evaluation of a perceptual-gestural activity expressing multiple skills being used. In addition to this, this ill-defined knowledge problem also affects the rating of a situation's utility with respect to the learning of these skills, and the learning task itself must be approached as ill-defined.

5.2

The ill-defined problem of performance evaluation related to enactive learning of non-technical skills Enaction states that knowledge emerges from the mutual modifications between a learner and a world, therefore, in order to learn, an individual has to be strongly coupled with the world, which in turn needs to react and modify itself in function of the individual's actions. The challenges raised by adopting an enactive approach to NTS learning in VE, illustrated in figure 2, can also be considered as the following ill-defined problems.

─ The sub-problems overlap, as any of the learner's actions on the virtual world will result in a change of the situation, which will either increase or decrease the importance of further actions from the learner. For example, in the case of a driving simulation, if the learner has correctly perceived the potential presence of a pedestrian dissimulated by a truck yet about to cross the road, he will be able to gradually slow down, therefore decreasing the degree of importance of another problem, such as the car tailgating him within which the driver might have been surprised by a brutal braking. Both of these aspects need to be considered together and not independently as their characteristics change simultaneously.

─ The task structure becomes ill-defined, and more accurately, it becomes analytical with the number of possible correct paths changing as a result of this pseudo-realtime coupling between learner and world. In driving for example, two drivers might adopt a similar strategy in response to a critical situation, but may implement this strategy with different degrees of efficiency. The way they perceive a situation and its degree of criticality is mediated during the course of their perception-action loop; this perception-action loop is in turn mediated by their technical and non-technical skills and by the perception of their own performance. Such a variability needs to be taken into account for the system to interact with the learner's actions, or in other words, to determine which feedback the VE will produce. Rather than a definite task structure, the issue is to model the singular experience of a learner trying to maintain his or her TS in front of a critical situation. Following the coupling envisioned in figure 2, the role of the ITS is then to drive the learner in a personalized "journey through criticality", assessing the coverage of a number of critical situations, and the involvement of a number of NTS.

Fig. 2. The coupling between user and system can be found at any stage of the training session. Behaviours (i.e. successions of perceptual-gestural activities) from the learner are processed and result in a series of traces. After a given critical situation is over, the performance perception should be double: the learner evaluates his own performance based on his perception of his behaviour during the situation, while the system uses the traces in order to evaluate TS and NTS. Experiencing a critical situation, the learner's TS and NTS level evolve and in parallel, the system adapts to this evolution by proposing a relevant new critical situation. While unfolding, this new critical situation will be perceived by the learner which will generate more perceptual-gestural activity, i.e. new behaviours.

A further look into these two characteristics of an ill-defined problem, which are specific to our interaction-centred approach, can be found in a more recent breaking down of ill-defined problems proposed by Nguyen-Thinh et al. [START_REF] Le | Operationalizing the continuum between well-defined and ill-defined problems for educational technology[END_REF]. The authors choose to look at learning as a succession of problems to solve in order to determine their degree of ill-definedness. Teaching domains become more or less ill-defined depending on the size of the solution spaces to a certain task. This solution space depends on the number of possible solution strategies, quantifying the existing approaches to solve a given problem, and the number of possible implementations for all of these strategies. At the most well-defined end of the continuum, well-defined problems have only one solution strategy which can be implemented only in one precise way. At the opposite side of the spectrum, a problem such as "the design of an investment simulation system" have an undetermined number of solution strategies and implementations [START_REF] Le | Operationalizing the continuum between well-defined and ill-defined problems for educational technology[END_REF]. Determining the position of a problem in this continuum can give an insight as to which technique should be best used in order to teach a problem. Because of sub-problems overlapping and the task being analytical, we ask that there must be quantifiable number of appropriate solution strategies in response to a given critical situation, but an indefinite number of ways to apply these strategies. For example, a driver may have braked after a single glance at an incoming danger, while the other may have focused his gaze specifically on it before doing so. They will have applied the same strategy in different ways.

Following [START_REF] Le | Operationalizing the continuum between well-defined and ill-defined problems for educational technology[END_REF] ranking of ill-defined problems in a continuum, we see that similar challenges with regards to performance evaluation have already been treated by the use of hybrid approaches including systems and model tracing for the more defined aspects of the problem-solving task, and datamining approaches in order to learn the more uncertain parts [START_REF] Fournier-Viger | A knowledge discovery framework for learning task models from user interactions in intelligent tutoring systems[END_REF]. These approaches however focus solely on the evaluation of a learner's performance. In our case, because the domain in itself also has ill-defined specificities, the learner's performance will need to be looked at from the scope of his knowledge state and the situation characteristics, in order to determine the actual influence NTS had in such a performance. This influence may hold with different degrees: intuitively, the effect of situation awareness or stress management on the learner's performance may appear very different. The situation characteristics may also result in varying degrees of criticality impacting the learner's performance, depending on the learner's sensitivities to a situation's characteristics. Such an approach is necessary in order to provide the more relevant feedback and select the more appropriate new learning situation given the specificities of each learner.

Conclusion

In this paper, we have shown the challenges raised by the teaching of NTS during critical situations inside of a virtual world and showcased why, given the characteristics of such skills, it is necessary to adopt an interaction-centred approach coupled with a modelling of knowledge, in order to maximise efficiency and to explore as many dimensions of criticality as possible. We have highlighted the reasons why such a combined approach is an ill-defined problem, both from the point of view of the interaction between the learner and the virtual world, and the point of view of knowledge modelling.

We have seen that some aspects of our problems were already partially explored in the ITS literature. For example, TELEOS [START_REF] Chieu | Student modeling in complex domains: Exploiting symbiosis between temporal Bayesian networks and fine-grained didactical analysis[END_REF] deconstructed a technical activity (namely the gestures of a surgeon in orthopaedic surgery) as a coupling of different types of knowledge in order to target the best feedback. CANADARMTutor [START_REF] Fournier-Viger | A knowledge discovery framework for learning task models from user interactions in intelligent tutoring systems[END_REF] used a hybrid approach including educational data mining techniques in order to learn a number of correct behaviours for the manipulation of a robotic arm, a task performed in a virtual environment showing a large realm of different possibilities. Both of these works shared some characteristics of ill-defined domains similar with ours, yet CANA-DARMTutor focused exclusively on the perception of a technical performance, while TELEOS aimed at proposing the most appropriate knowledge-type based feedback. The learning of NTS in critical situations inside of a virtual world will need to enfold both the performance analysis aspects of CANADARMTutor and the knowledge modeling assets of TELEOS, while considering a new aspect of an ill-defined problem, which is taking into account the merging barriers between technical and non-technical expertise.

This report is the extended version of the paper "An Approach to the TEL teaching of NonThe research was supported by the MacCoy Critical project (ANR-14-CE24-0021).


N Yoshikawa
email: yoshin@material.tohoku.ac.jp

High frequency electromagnetic field energy application to materials' processing and green technology

Keywords: High frequency, induction, electromagnetic field, energy, material processing, green technology

Application of electromagnetic (EM) field of 10 4 Hz to metals generates induction current, which brings about Joule heating and Lorentz force. Magnitude of magnetic field in the metal surface layer is much larger than the electric field, and hence it is interpreted that induction current is generated by the alternating magnetic field. Induction heating is applied for melting and stirring of molten metals and is utilized for recycling of metals and production of alloys. At 10 5 Hz or more, induction heating of glasses are performed and applied for glass solidification of hazardous wastes. Discussion is made for selection of the induction heating frequency of non-metals, which have considerable conductivity (but less than metals). Heating of non-conductive materials also becomes possible by dielectric loss mechanism, such as drying of woods and heating of conducting ceramics. Above 10 9 Hz range (microwave and millimeter wave), non-conductive organics, inorganic materials and biological bodies (containing water) are also heated by dielectric loss mechanism. Electric field becomes important in this mechanism. Recently, researches of metal and conductive materials' heating are performed using a single mode cavity. Depending on the substances, it is possible to select the usage of either electric or magnetic field. Specific applications are currently being explored. Above 10 12 Hz (tera herz, far infra-red) range, electromagnetic wave has a property of light, and electric field contribution is more significant than that of magnetic field. Recently, interaction between the electric field of light and nano-sized metal particles becomes a hot research area for various applications.

EM field energy application to materials' processing and green technology 1. Frequency range less than 10 5 Hz Direct current (DC: 0 Hz) is applied for heating some conducting materials. Alternative current (AC) at a commercial frequency (50 or 60 Hz) is utilized for heating, as well. Energy consumption of these heating processes is through the Joule heating. However, if they are applied to heating large metal bodies, large current flows, and results in too much energy consumption. Therefore, direct current heating of metals is limited. On the other hand, induction frequency of an order of ~10 4 Hz is usually utilized for metal heating. This frequency is determined considering the optimum between the induction current increase with the frequency and the skin depth thickness (δ) decrease as the frequency increase. δ is expressed by Eq. 1, where σ, µ are electric conductivity, magnetic permeability of the metals and ω is an angular frequency (ω = 2πf, f : frequency)

δ = 2 ωµσ (1)
Magnitude of magnetic field (H) in the metal surface layer can be compared with that of the electric field (E) by Eq. 2 [START_REF] Jackson | Classical Electrodynamics[END_REF], where c is a light speed and λ is a wave length (in vacuum). At 10 4 Hz, δ/λ is estimated to 1.7x10 -7 , suggesting that the magnetic field is much larger than the electric field, and it is generally interpreted that induction current is generated through alternating magnetic field (variation with time).

E/(µHc) ~ ωδ/c ~ δ/λ (2)
Experimental and simulation studies of metal heating and liquid metal flow are one of the major subjects of this conference. Analysis of the Joule heat and the pinch force (F: Eq. 3) by the induction current are performed, both of which are generated within the skin depth (δ), leading to melting and stirring of metals, respectively. Pinch force (F) is raised by a total current (J). J is expressed by Eq. 4 in terms of a current due to the flowing metal at velocity of v under a high frequency magnetic field ( B = ∇ × A ) and a induction current (j: the second formula in Eq.4), where A and φ are a vector and scalar potential, respectively. F and Q are incorporated into flow and heat transfer equations for establishing the full coupling of EM-flow-heat transfer model.

F = J x B (3) ( ) ( )       - ϕ ∇ - σ       - ϕ ∇ - × ∇ × σ = × σ ∂t ∂ , ∂t ∂ = A = j A A v E + B v J (4) Q = σ|j| 2 /2 (5)
2. Frequency range at 10 5 ~ 10 9 Hz In this frequency range, EM energy field is not usually utilized for bulk metal heating since penetration depth is small. Namely, only metal surface heating cannot raise the temperature sufficiently. On the other hand, heating of non-metals (having lower conductivity than metals) are being performed at this frequency range. Some conducting ceramics such as ferrite particles are heated and utilized for the medical application [START_REF] Hirazawa | Proc. of 6 th Int. Conference on Electromagnetic Processing of Materials[END_REF]. Liquid Si has high conductivity having the same order as that of metals (metallic conductivity). Nevertheless, heating of liquid silicon is conducted at the frequency around 3MHz [3,[START_REF] Wakabayashi | yogyo kyoukaishi[END_REF]. To the author's knowledge, there are few descriptions in the literature discussing selection of this frequency for Si. There are much less arguments on the optimum frequency of induction heating of non-metals, such as glasses and other non-metallic liquids. One of the reasons is due to the fact that very large variation of the electric conductivity with temperature and the frequency, while metal conductivity does not have large change.

Here, it is intended to discuss induction heating and stirring of glass, which is utilized for melting and recycling of glasses, glass fibers, glass consolidation of radioactive matters, melting / homogenization of glass composition. Electric conductivity is low at low temperature, as the soda-lime glass data [5] indicated in Fig. 1(a). Therefore, induction heating of the glasses is not possible unless it is melted by means other heating methods, once, such as by a burner. Generally, induction frequency range in the industrial operation is between several hundred kHz and several MHz, and the temperature of 1000~1500 o C. The electric conductivity is an order of 10 1~2 [S/m], which is much lower than that of metals. The penetration distance can be estimated, assuming the frequency at 1MHz and σ = 10 [S/m] to be 16cm. The distance is much larger than the metals. However, relatively less reports on the induction current distribution is found in the previous literature by the analysis of EM field calculation. Viscosity of glasses also has large temperature dependence and is fairly larger than that of metals (for example: liquid metal order of ~10 -3 [Pa . s], glasses order of 10 0 [Pa . s] at the operation temperature), as an example of the soda-lime glass [6] illustrated in Fig. 1(b), together. Thus, even if Lorentz force is generated by induction heating, induction stirring to overcome the high viscosity is not easy. Some theoretical studies for glass stirring are made and discussed the flows raised by a natural convection or by a forced convection of impeller stirring [7,[START_REF] Nacke | Proc. of 4 th Int. Conference on Electromagnetic Processing of Materials[END_REF]. There are some numerical studies [START_REF] Yoshikawa | [END_REF], in which Lorentz force contribution to stirring has been taken into consideration, however, degree of its contribution has not been quantitatively discussed in detail. At least, it should be noted that Lorentz force contribution to stirring of liquid glass could only be possible at very high temperature of high conductivity and low viscosity conditions are attained, as discussed above. Electric conductivity of liquid glass has frequency dependence, such as too low at low frequency below 10 5 Hz. In order to account for the frequency dependence of the conductivity and to design the heating and stirring operations, impedance analysis of the heating objects and the systems is required, which is usually discussed in terms of equivalent circuits consisting of capacitance, inductance and resistance components. The capacitance of the heating objects is related with the permittivity (ε: dielectric constant) of the materials. In discussing their contributions to heating, ambiguity in separation of the rightest hand side of Eq.6 becomes a problem, where ε r is a relative permittivity and is defined as ε/ε 0 (ε 0 is a permittivity of vacuum). The imaginary part of the rightest hand (related with the energy dissipation) contains a dielectric loss factor ( # ε r ") and a conduction (induction current) loss term. Experimentally measured value is their sum (i is the imaginary unit):

ε ρ = ε ρ ' -ε ρ "i = ε ρ ' -( # ε ρ "+σ/(ε 0 ω)) i (6)
Therefore, it is inferred that glass heating by high frequency EM field could be not only by Joule heating of induction current but also by dielectric heating, though no enough arguments have been presented so far. Moreover, it is not easy to measure the permittivity at high temperature. Thus availability of glass permittivity data in liquid state is very limited, especially. In this article two plots are demonstrated for discussion on the ε r " contribution to the heating at high temperature. The first is a temperature dependence of ε r ' and ε r " of soda-lime glass at 2.45GHz [START_REF]Dielectric Materials and Applications[END_REF] in Fig. 2. Value of ε r " increases with temperature. Although the shown temperature is not high for melting of soda-lime glass, and the frequency is higher in a GHz range. In Fig. 3, permittivity of solid steatite ceramic ε r " also increases with temperature at 10 5 Hz and becomes high enough for the dielectric heating. Here, in both cases, it is hard to determine whether increase of ε r " is caused by an increase of permittivity imaginary part ((genuine) # ε r ") or by a conductivity σ in Eq.6. The apparent imaginary part of the relative permittivity ε r " in Eq.6 is estimated if assuming σ = 10 [S/m] (1250K of soda-lime glass, Fig. 1a) and at 10 5 Hz, so σ/(ωε 0 ) corresponds to ε r " = 1.8x10 6 [-], which could be a very high dielectric loss factor, giving rise to dielectric heating. In this case, the electric conductivity σ, (having a relationship of σ = ωε") is called dielectric conductivity [START_REF] Yoshikawa | [END_REF]. Physical image of the difference in conduction manner might be a movement of charge carrier for long distance, but short range movement in the dielectric current (or displacement current).

In ionic bonding substances, many electric conduction mechanisms exist. Ion mobility in solid crystals could become larger in this frequency range (10 5 ~ 10 9 Hz) depending on temperature. There are many examples of materials where transition from the insulating ionic crystals to electric conductor or semi-conductor occurs, depending on the competitive contribution between ionic and electronic conduction. Therefore it is pointed out that heating of nonmetallic materials by EM field energy and the energy dissipation processes has to be discussed from a view point of the EM field energy interaction with materials itself in this frequency range. 3. Frequency range at 10 9 ~ 10 12 Hz This frequency range is called microwave, millimeter wave and far infra-red (Terahertz) wave, from the lower frequency in this order. Non-conductive organics, inorganic materials and biological bodies (containing water) are heated by dielectric loss mechanism. Heating by microwave EM field energy has been applied to production of various industrial materials, foods, processing and environmental treatment technologies. Microwave generated by an oscillator is multiply reflected on the metal walls in the applicator (chamber) and is aimed to be irradiated to the heating objects homogeneously. This is attempted not only in the domestic microwave oven, but also in the industrial microwave heating facilities.

On the other hand, recently, researches of metal and conductive materials' heating are performed using a single mode applicator. Depending on the substances, it is possible to select the specimen to place in a microwave cavity of either electric and magnetic field maximum position (Fig. 4). The geometries of the electric (E) and magnetic (H) field distributions in a single-mode applicator are also shown in Fig. 4. Generally, EM field energy is expressed as contribution of three heating mechanisms as expressed by Eq. 8. By using a single mode microwave applicator, small enough specimens can be placed and heated at either E-field or H-field maximum positions. It is possible to separate the heating mechanisms or discussion on their interaction with EM field.

2 2 2 2 1 2 1 2 1 Q H E E µ ′ ′ ω + σ + ε ′ ′ ω = (7)
Joule heating of metals by induction current is also possible in this frequency range, but the penetration distance in the metal is of an order of micron meter, therefore, metal heating is limited to the films or powders. The metal film or particles are well heated in a H-field maximum position. High frequency magnetic field raises the current, but the induction current is written in terms of electric current driven by E-field in Eq.7 (second term). The third term in Eq. 7 is the mechanism originated in inherent magnetic mechanisms of materials [13]. On the other hand, dielectrics such as water and some organics, etc are heated better in E-field maximum positions. Ferroelectric ceramics are well heated, as well. This is a contribution of dielectric mechanism expressed as the first term in Eq. 7. Although single mode heating is limited to specimens of small size (~1cm at 2.45GHz, larger specimen is possible at the lower frequency, 0.915GHz, for example), specific applications using a single mode cavity are being explored. In metals, free electrons experience collisions at finite temperature. The collision frequency is of an order of 10 13~14 [s -1 ], irradiation of EM field of this frequency coincides with that of electron collisions and has an influences on the electric conductivity. An imaginary part of conductivity appears (Electron conduction in metals exhibits a complex conductivity). It is of interest to describe behavior of nano-sized metal particles, because they become dielectric at the EM frequency of 10 15 Hz (visible light range). Nano-sized metal particles have large surface area comparing with their volume. If an electric field is applied, electrons in surface area displace as schematically illustrated in Fig. 5. This change in electron distribution is regarded as the polarization, thus they become dielectric. The surface electron movement or displacement have some resonance at certain EM frequency, and results in large absorption of (EM field) energy. Absorbing of EM field energy varies by adsorption of some molecules on the metal surface. This phenomenon is applied for sensing of foreign molecules.

E-field distribution H-field distribution

Summary

In this study, interaction of EM field energy with materials was discussed by classification with respect to the frequency ranges. Contribution of electric and magnetic field differs depending on the frequency and the materials, such as either an electric conductor or having dielectric polarizability. Magnetic field contributes to liquid metal heating and stirring at 10 4 Hz. Electric field contribution to heating of liquid glass (dielectric heating) at 10 5 Hz in addition to the induction current heating was discussed. On the other hand, field contribution is separated and discussed by using microwave cavity at 10 9 Hz. Electric field becomes major interaction above 10 12 Hz.

Fig. 1 :

 1 Fig.1: Temperature dependence of (a) electric conductivity[5] and (b) viscosity[6] of soda-lime glass.

Fig. 2 : 3 :

 23 Fig. 2: Temperature dependence of permittivity (ε ρ ', ε ρ ") Fig. 3: Temperature dependence of permittivity of of soda-lime glass [10] at 2.45GHz. steatite ceramics at 10 5 Hz [11].

Fig. 4 : 5 :

 45 Fig. 4: Distribution of electric and magnetic field distributions Fig. 5: Electron displacement in nano-sized metal in TE103 microwave cavity. particles [14]. 4. Frequency range above 10 12 Hz At this range of frequency, EM field has a feature of light. E-field interaction with materials is much important in light.In metals, free electrons experience collisions at finite temperature. The collision frequency is of an order of 10 13~14 [s -1 ], irradiation of EM field of this frequency coincides with that of electron collisions and has an influences on the electric conductivity. An imaginary part of conductivity appears (Electron conduction in metals exhibits a complex conductivity). It is of interest to describe behavior of nano-sized metal particles, because they become dielectric at the EM frequency of 10 15 Hz (visible light range). Nano-sized metal particles have large surface area comparing with their volume. If an electric field is applied, electrons in surface area displace as schematically illustrated in Fig.5. This change in electron distribution is regarded as the polarization, thus they become dielectric. The surface electron movement or displacement have some resonance at certain EM frequency, and results in large absorption of (EM field) energy. Absorbing of EM field energy varies by adsorption of some molecules on the metal surface. This phenomenon is applied for sensing of foreign molecules.

Acknowledgement

This study was partially supported by Part of this work was financially supported by a Grant-in-Aid from Ministry of Education, Sports, Culture, Science and Technology, Japan, Priority Area (18070002,(2006)(2007)(2008)(2009)(2010).


V M Volgin
email: volgin@tsu.tula.ru

V V Lyubimov

A D Davydov

Effect of axial magnetic field on mass transfer to cylindrical cathode under mixed convection of binary electrolyte solution

Keywords: Cylindrical cathode, mass transfer, mixed convection, magnetic field, binary electrolyte

Effect of axial magnetic field on mass transfer to cylindrical cathode under mixed convection of binary electrolyte solution

Introduction

The effect of convection on the heat and mass transfer to the cylindrical solids has been much studied [START_REF] Sumer | Hydrodynamics around cylindrical structures[END_REF][START_REF] Vyver | [END_REF]. The convection can raise significantly the mass-transfer rate to the cylindrical electrode in the metal electrodeposition. However, the convection usually distorts the distribution of the deposit and produces a significant difference between the thickness of the deposit layer at the upstream and downstream parts of a cylinder [START_REF] Vyver | [END_REF]. The nonuniformity of deposit thickness can be decreased by applying a magnetic field, which generates the solution flow [3]. This flow is generated by the Lorentz force, which arises from the interaction between electrolytic current and magnetic field [4]. In [5], the numerical simulations of electrochemical plating of a single cylinder with forced convection for Reynolds number 10 with a longitudinal magnetic field were performed. This case gives not only a good homogenization of the deposit but also a significant improvement of the overall mass transfer rate. The alternating magnetic field appeared to be more effective. It can be concluded that, by using a magnetic field, it is possible to considerably improve this kind of electroplating processes. In [5], the case of electrodeposition from the solution containing an excess of supporting electrolyte was considered. This allowed the authors to ignore the migration transfer of electroactive cations and the variation of electrolyte solution conductivity. In the case of binary electrolyte or a solution with a low concentration of indifferent electrolyte, the above assumptions cannot be used. In addition, along with the forced convection, the natural convection of solution can have an effect on the mass transfer [6,7]. Here, the effects of a magnetic field on the mass transport at a cylindrical electrode are examined under mixed convection of binary electrolyte solution.

Mathematical model

Fig. 1 shows the geometry of domain used for modeling of mass transfer to the cylindrical cathode. The Navier-Stokes equations for incompressible viscous liquid in the Boussinesq approximation with regard for the Lorentz volume force, the transport equations of cations and anions, and the electroneutrality conditions are used as the mathematical model. As a result of eliminating the migration terms from the ionic transport equations and passing to the dimensionless variables, the mathematical model takes the following form:

        0 A Sc Re 1 0 1 Sc Re Ra A Sc Re M Re 1 2 2 D                                   C C C C C C C C P g z V V e e V V V V   (1)
where V is the dimensionless electrolyte solution velocity; P is the dimensionless pressure;

C is the dimensionless concentration of electroactive cation;  is the dimensionless potential;  is the dimensionless time;

  / Re 0 v d  is the Reynolds number; ) /( Sc D    is the Schmidt number;   ) /( M 2 0 2 2 1 1 , 1 1 D D d B D z D z Fc z b    is the dimensionless magnetodiffusion parameter;   ) /( / Ra , 1 , 1 3 D c c gd b b      is the Rayleigh number; ) /( ) ( 2 2 1 1 2 1 D z D z D D A    is parameter;
z e is the unit vector directed along Z axis;

    2 2 1 1 2 1 2 1 / D z D z D D z z D   
is the effective diffusion coefficient of binary electrolyte;  is the dynamic viscosity of binary electrolyte solution;  is the density of binary electrolyte solution; v 0 is the rate at the inlet boundary (Inlet); g is the gravitational acceleration; B 0 is the applied magnetic field is taken as a unit pressure; a ratio between the cathode diameter and the rate at the inlet boundary (d/v 0 ) is taken as a unit time; R is the gas constant; T is the temperature. The boundary conditions are as follows:

U C x     Inlet Inlet Inlet , 1 , e V (2) 0 , , 0 , 0 Outlet Outlet Outlet Outlet           P X X C X V (3) H Y H Y H Y H Y H Y H Y C C               , , V V (4)         0 , 1 exp exp , 0 Cathode 2 0 Cathode Cathode                        N C z N C n n C I N C   V , ( 5
)
where U is the dimensionless applied voltage (a potential difference between the inlet boundary and cathode); 0 i and

    2 1 , 1 1 1 0 2 0 / z z c D Fz di z I b   
are the dimensional and dimensionless exchange current densities, respectively; n is the number of electrons exchanges in electrochemical reaction; α is the transfer coefficient of cations; N is the unit normal vector to cathode surface. Equations ( 2) and (3) prescribe the boundary conditions at the inlet and outlet, respectively; equations (4) correspond to the boundary conditions on the horizontal periodical boundaries; and equations ( 5) are the boundary conditions on the cylindrical cathode. It is assumed that the anode is placed far from the cathode and has no effect on the mass transfer to the cathode.

Method of numerical solution

The set of equations is solved numerically. The solution procedure is based on the finite-element discretization of the transport equations and the continuity equation for an incompressible fluid, resulting in a discrete set of equations for velocity, pressure, concentration and potential. The numerical scheme is based on the pressure correction method where a correction to the pressure field is computed such that the divergence of the velocity field is forced to be zero and the continuity equation can be satisfied. At each time step the nonlinear equations are solved by iteration. The convection velocity and other parameters are evaluated at the previous iteration and a linear equation system is formed for each variable. The linearized difference equation system is solved by an iterative solution method. The dimensionless stream function is calculated by the following equation:

    , , , Y) P(X, Cathode     dX V dY V Y X Y X  (6)
where P(X,Y) is a point inside the computational domain; V X and V Y are the velocity components along X and Y axes, respectively.

Results

The modeling is performed at the following values of parameters: z 1 =1; z 2 =-1; A=-0.5…05; I 0 =1000; n=1; α=0.5; U=10…100; H=5…20; Re=1…20; Sc=1000; M D =0…10 5 ; Ra=-2.5e6…2.5e6. To provide the independence of simulated results from meshing the computational domain into the finite elements, the test computations are performed; as a result, a grid with 27000 elements was chosen. A fine mesh is used near the cylinder in order to get at least 20 cells in a thin concentration boundary layer (Fig. 1b). The grid step near the cathode surface is taken to be 0.0002. Fig. 2 gives the results of modeling mass transfer in the absence of external magnetic field under the forced (Figs. 2a and2b) and mixed (Figs. 2c -2f) convection of binary electrolyte solution at A=-0.1; U=50; H=5; Re=10. In Fig. 2, the dark areas correspond to the lower concentration of electroactive ion. From the simulated results it follows that the natural convection of electrolyte solution has a pronounced effect on the mass transfer to the cylindrical cathode and, under certain conditions, allows one to enhance the uniformity of current density distribution over the cathode surface. The current density in the upstream point (Fig. 1) only slightly depends on the natural convection of solution. In the downstream point, the current density increases both at the positive and negative Rayleigh numbers. The most uniform distribution of current density over the cathode surface is achieved at negative Ra (Figs. 2e and2f). In this case, a degree of nonuniformity of current density distribution decreases by more than two times.

To develop the method of alternating magnetic field, here, it is assumed that the magnetic field varies in the following manner: (7) where M D,0 is the amplitude of variation of parameter M D ; T is the dimensionless period of variation of magnetic field; and a is the coefficient characterizing the constant component of magnetic field. From the calculated results it is seen that the most uniform distribution of current density over the cathode is achieved when a constant and periodically varying magnetic fields are imposed simultaneously. Fig. 3 gives an example of the variation in the solution flow during a single period. T was taken to be longer than the dimensionless diffusion time scale , the slow adjustment of the diffusion layer cannot provide a considerable increase in the mass-transfer rate and uniformity of current density distribution over the cathode surface. At very long T comparable with the total duration of electrodeposition, a deposit asymmetrical about the horizontal axis forms. At the medium periods of magnetic field variation, the best results can be obtained. As a result of superposition of alternating and constant magnetic fields, the conditions of mass transfer on the downstream part of cathodic surface can be improved and the uniformity of distribution of current density averaged over the period of magnetic field variation can be enhanced. A comparative analysis of metal electrodeposition in different kinetic modes showed that, in the case of electrochemical kinetic mode (the Butler-Volmer equation is used), the effect of external magnetic field on the uniformity of current density distribution is weaker than in the case of diffusion limiting current mode.

  , ) / 2 sin( M M D,0 D a T   

Conclusions

The numerical modeling yielded the dependences of the rate of mass transfer to the horizontal cylindrical cathode and the uniformity of distribution of current density over the electrode surface on the main parameters of the system under the forced and mixed convection of binary electrolyte solution. It is shown that the natural convection of electrolyte solution allows one to enhance the uniformity of current density distribution over the cathode surface. The effect of constant and periodically varying uniform magnetic field on the mass transport is studied. It is found that the most uniform distribution of current density over the cathode is achieved when the constant and periodically varying magnetic fields are imposed simultaneously.

  vector in gravity direction; d is the diameter of cylindrical cathode; F is the Faraday constant; of electroactive cations in the bulk electrolyte solution; m z is the charge of ions of the m-th type; m D is the diffusion coefficient of ions of the m-th type; m is the subscript (1 stands to the electroactive cation and 2 stands to the nonelectroactive anion);

Fig. 1 :

 1 Fig. 1: (a) Scheme of computational domain and (b) mesh with boundary layer near cathode. When we passed to the dimensionless variables, d is taken as a unit length; v 0 is taken as a unit rate; b c , 1 is taken as a

Fig. 2 :

 2 Fig. 2: (a, c, e) Distributions of dimensionless concentration of electroactive ions and (b, d, f) distributions of dimensionless stream function during electrodeposition on cylindrical cathode: (a, b) Ra=0; (c, d) Ra=2.5e6; (e, f) Ra=-2.5e6.

Fig. 3 :

 3 Fig. 3: Flow structure near cylindrical cathode at M D,0 =10000, T=200; a=0.25; Ra=0: (a) τ=mT; (b) τ=(m+0.25)T; (c) τ=(m+0.5)T; (d) τ=(m+0.75)T.

Acknowledgment

Financial support from Ministry of Education and Science of the Russian Federation under project no. 1096 of the Basic Part of the State Program and financial support from Russian Foundation of Basic Research under project no. 13-08-97562 are gratefully acknowledged.


O Kazak
email: oleg.kazak@tu-ilmenau.de

B Halbedel
email: bernd.halbedel@tu-ilmenau.de

Approaches for modelling electromagnetic parameters in milling demonstration plant of organic agents

Keywords: electro mechanical milling, magnetic field, electromagnetically force, power consumption, simulation

This paper is devoted to the numerical simulation of electromagnetic parameters in electromechanical milling laboratory plant EMZ-LAI. The physical and mathematical descriptions of electromechanical milling laboratory installation are presented. The methods and approaches for modelling the electromagnetic parameters in standard software packages are worked out. The obtained simulation results have shown good agreement with experimental measurements and the differences of the results are around 5 %.

Introduction

In recent years the improvements of mills in numerous industrial applications such as fine milling of organic agents has increased steadily [START_REF] Halbedel | Potenziale des Elektromechanischen Zerkleinerungsprinzips[END_REF][START_REF] Halbedel | Technische Keramische Werkstoffe, John von Freyend GmbH[END_REF]. The milling process is very complicated and has high power consumption so that is why the interest exists to improve the efficiency of this process by using new electromechanical milling process. The electromechanical principle has high potential in many applications but the optimisation of magnetic field distribution in the exciter systems and the magnetic force distribution in the process room with suitable models based on numerical simulation are still needed. The laboratory plant EMZ-LAI has shown very good characteristics of milling process. The power consumption is very low because power supplied direct to the grinding media. The biggest part, around 74 %, of all supplied power in machine going to milling process and only 23 % to Ohmic losses, 3 % to Iron losses in the sheets [START_REF] Halbedel | Potenziale des Elektromechanischen Zerkleinerungsprinzips[END_REF]. The main parameters in such machines for milling are the magnetic field intensity and the electromagnetic force distributions in the working chamber. For future development of this principle and design new machines it is very important to make a suitable model for numerical simulation and optimisation. This model is developed in ANSYS Maxwell and tested by the convergence on the calculation mesh, with different software setup and analysis type, different applied currents. Simulations are carried out in 2D and 3D statements. Verification is made by comparing results provide in ANSYS Maxwell and COMSOL Multiphysics as well as with experimental measurements in the laboratory installation.

Electromechanical milling process

The electromechanical milling principle is based on the movement of hard magnetic milling beads under electromagnetically force F B generated by interaction between the gradient of magnetic field B and the magnetization M of the milling beads as it shown on the fig. 1. The generated force is given by Eq. ( 1):

  BM F p B    (1)
where

M V dV   pM , B    grad B , ,, , M M r M pp     p .
The milling beads must have a permanent magnetization M. Additionally, if the magnet field gradient is time-and localdependent, than an intensive relative movement of the milling beads is induced which generated different types of mechanical stresses so that the novel electromechanical milling principle can be used for disintegration of biomass, dry or wet grinding of raw materials and autogenously grinding of ferrites [START_REF] Halbedel | Potenziale des Elektromechanischen Zerkleinerungsprinzips[END_REF]. Electromechanical milling laboratory equipment EMZ-LAI utilises a rotating magnetic field in process room between outer and inner exciter systems. The schema of EMZ-LAI is presented on the fig. 2. Their design is analogical to AC motors with big air gap between outer (ESI) and inner (ESII) exciter system. Total input (respectively active) power P W of the electromechanical mill is dissipated in the following parts:  P v1 -Winding and core losses in the exciter systems,  P δ -Air-gap power,  P v2 -Hysteresis losses in the hard magnetic grinding media,  P vZ -Milling losses and  P N -Net power of the milling (released interfacial energy due to surface growth).

Model for numerical simulation of electromagnetic parameters

The numerical simulation of this machine can be carry out in a similar approach as [START_REF] Lindner | Simulation of magnetic suspensions for HGMS using CFD, FEM and DEM modeling[END_REF] by decupling this problem in two parts: simulation of electromagnetic parameters of machine inside air gap in ANSYS Maxwell or COMSOL Multiphysics, then transfer this data as data file to the discrete element method (DEM) based software and carry out simulation of the moving milling beads inside air gap. This approach can be presented as closed loop: 1) Modelling of electromagnetic fields in EMZ machine without milling beads in ANSYS Maxwell or COMSOL Multiphisics (at first step check-up by experimental measurements); 2) Transfer results of electromagnetic fields to DEM based software; 3) Modelling of milling beads movement under magnetic force (at first step check-up by experimental results); 4) Analyse of milling beads movement and optimize parameters of EMZ machine. Optimization of the EMZ machine can be carry out in two steps:

1) Experimental determination of the effective field distribution in the air gap for the milling and 2) determination of the new design which generates the same effective field distribution values in the air gap with the lowest possible losses. Modelling of electromagnetic fields in EMZ machines is described by Maxwell's questions (Eq.( 2)):

B E t      , 0 B   , D HJ t      , D    . ( 2
)
To build model for simulation of electromagnetic field in ANSYS Maxwell it is necessary to include the design of iron sheets of inner and outer systems of EMZ-LAI machine. Fig. 3 presented iron sheets in 2D. The main geometrical parameters are outer diameter with 322 mm and the air gap distance with 25.5 mm. The number of slots of outer system is 48 and inner is 36. To carry out simulation of the electromagnetic field it is necessary to take into account magnetic parameters of iron sheets. The outer system was made from TKES 800-50A and inner from TKES 400-50A steel with special magnetic properties.

The outer and inner coils system are located in the iron sheets and connected parallel to each other to 3 phase current.

The connection of inner (ESI) and outer (ESII) systems as well as the used electrical measurement system are presented on the fig. 4. Symmetrical time-dependent current distribution according to the phase connection is presented by following equations: cos( )

A i I t    , 2 cos( ) 3 B i I t     , 4 cos( ) 3 C i I t     . ( 3
)
The average magnetic field strength in air gap H δ dependents on the root mean square (RMS) of the phase currents in ESI (I A,I ) and ESII (I A;II ) and is given by following equation:

      ,, / 2815* 2496* A I A II H kA m I A I A   . ( 4
)
The ratio of RMS values in inner and outer system is fixed by: 6 the distribution of calculation mesh for the EMZ-LAI and outer space with 9688 elements is shown. The calculation domains split into elements uneven: parts in the exciter systems with large gradient of electromagnetic parameters, here the sizes of the cells are very small and outer space with small gradient of electromagnetic parameters, here the size of elements increases. According to special magnetic properties of iron sheets outer and inner system the outer space diameter is very small and around two diameter of outer magnetic system.

The mesh convergence is presented on the fig. 7 as dependency of error from the finite element number. As can be seen from this dependence with number of elements 13258 the error amounts 1.78 %. This result is suitable for simulation and all further simulations are carried out with this number of elements.

Results of electromagnetic parameters simulation

The simulations of electromagnetic parameters are carry out for following typical magnetic field strengths in air gap H δ = 50, 70 and 100 kA/m with the frequency f = 50 Hz. The main parameter of electromagnetic simulation result ANSYS Maxwell is the magnetic potential A. The distribution of magnetic potential for H δ = 50 kA/m is presented on the fig. 8. From this distribution we can see that the magnetic potential in the air gap between outer (ESI) and inner (ESII) coils systems changes azimuthally and has 2p=4 poles. These 4 poles rotate with constant velocity n which can be estimated from AC motor theory with f n p  .

To verify the obtained simulation results the experimental measurement of magnetic flux density distribution in the middle of EMZ-LAI air gap are carry out with the help of Hall Probe MNT-4E04-VH (Lake Shore) and Gauss meter 421 (Lake Shore). The results of this experimental measurement in comparison with simulation data for the azimuthal and radial components are presented in the Table 1. As can been seen, the relative differences amount maximal up to 7 %. This difference comes from influence of the real magnetic properties and geometry of the iron sheets, also from the discretization of the coil distribution. The differences of the magnetic flux density magnitude B mag obtained in ANSYS Maxwell and COMSOL Multiphisics are approximately 3 %. The differences between results in 2D and 3D statement simulation in all parameters distribution in the middle cross section arise 2-3 %. That is why it is possible to carry out further simulation in 2D statement. The results of all comparison tests obtained with different software packages, in 2D and 3D statement and with experimental measurements prove the numerical model as well as approaches for numerical simulation of electromagnetic parameters of exciter systems for electromechanical mills.

Conclusions and outlook

Based on this results it is possible to make following conclusions:  the methods and approaches for numerical simulation of magnetic field in the ANSYS Maxwell and COMSOL Multiphysics are worked out,  it is shown possibility to check-up results of simulation with experimental measurements of electromagnetic fields. The next steps are:

 to find out the electromagnetic parameters from experimental data for an efficiently milling process,  carry out simulation for this parameters and determinate the magnetic field gradient for the optimal milling process and  based on known parameters to find out approaches for the design of the new machine .

Fig. 1 :

 1 Fig. 1: Force F B on a body with a magnetisation M in the gradient of magnetic field B.

Fig. 2 :

 2 Fig. 2: EMZ-LAIview with a cut section.

Fig. 3 :

 3 Fig. 3: Iron sheets of outer (ESI) and inner (ESII) systems of EMZ-LAI

Fig. 4 :

 4 Fig. 4: Electric connections of ESI and ESII to 3-phase: A, B and C.

Fig. 5 :

 5 Fig. 5: Coil distributions in the 2D cross section of the exciter systems.

Fig. 6 :

 6 Fig. 6: Mesh for numerical simulation.

Fig. 7 :

 7 Fig. 7: Mesh convergence dependent on used number of elements

TABLE 1 .

 1 Comparison of numerical results and experimental measurements of the RMS values of the magnetic flux density in the middle of the air gap at different average magnetic field strengths H δ and fixed frequency f = 50 Hz.

	H	B	B	relative	B	B	relative
	δ	r RMS	r RMS	difference	φ RMS	φ RMS	difference
	kA/m	simulation	experiment	%	simulation	experiment	%
		[mT]	[mT]		[mT]	[mT]
	50	43.73	43.45	0.64	5.75	5.31	7.65
	70	63.18	59.64	5.60	7.39	7.20	2.57
	100	94.97	89.04	6.24	9.95	9.27	6.83

Acknowledgment

The authors acknowledge financial support by the Federal Ministry for Economic Affairs and Energy (BMWi) in ZIM-Cooperation Project EMZ-W (KF2184744KO4).