Clovis Anicet Ouedraogo
email: ouedraogo@laas.fr

Samir Medjiah
email: medjiah@laas.fr

Christophe Chassot
email: chassot@laas.fr

A Modular Framework for Dynamic QoS Management at the Middleware level of the IoT Application to a oneM2M compliant IoT platform

Keywords: Internet of Things, Quality of Service, Middleware, Modular Framework, Dynamic deployment, Autonomic Computing

The Internet of things (IoT) has evolved exceptionally in recent years; enabling a large number of heterogeneous devices to be interconnected to users via the Internet. This new concept promises in a few years to interconnect billions of devices, which will generate many challenges on the infrastructure supporting these communications. One of these challenges is the satisfaction of the different QoS requirements of the applications. To address this challenge, we identified two bottlenecks with respect to the QoS, which are the networks and the intermediate entities (i.e. middleware) allowing the applications to interact with the devices. In this paper, we propose a modular framework to ensure the QoS of applications at the middleware-level through QoS-oriented mechanisms deployed dynamically and autonomously on the middleware entities. The benefits of this framework are presented through test scenarios in the vehicular transportation domain.

I. INTRODUCTION

The Internet of Things (IoT) is a new paradigm that particularly relies on new communication architectures and protocols, including the middleware (MW) level. To ensure interoperability between connected objects and applications, the oneM2M initiative proposed a distributed REST-based middleware service [1]. Through this MW, applications can collect data and/or trigger commands thanks to distant sensors and actuators through simple (e.g. http) requests (see Fig. 1).

Fig. 1. Overview of an IoT Middleware

These different applications have different requirements in terms of Quality of Service (QoS), and particularly bounded response times. These needs face two bottlenecks: the traversed IP networks, and the intermediate entities implementing the MW layer. In this paper, we address the problem of the bottleneck represented by the MW layer with regard to the QoS requirements of IoT applications.

To tackle this QoS problem, the approach which is explored in this paper is based on the dynamic (i.e. at design-time but also at runtime) and autonomous (i.e. without human interactions) deployment of software modules implementing QoS-oriented mechanisms at the MW level. This deployment is achieved seamlessly for the applications and the connected objects. Basically, the considered mechanisms act on the applicative traffic with the aim to differentiate their processing within the considered MW nodes.

Modular programming is a software design technique [START_REF] Yau | A Survey of Software Design Techniques[END_REF] that emphasizes separating the functionality of a program into independent and interchangeable modules, such that each one contains everything necessary to execute only one aspect of the desired functionality. A module interface expresses the elements that are provided and required by the module.

To implement the proposed approach, we consider in Fig. 2 a typical deployment infrastructure for MW-based IoT applications. Each application is accessed using a user terminal such as computers or smartphones. An IoT MW is linking the application to the physical sensors and actuators. The application backend as well as some MW entities are deployed in public or private Cloud. Some MW entities may be deployed within the Service Provider private infrastructure using dedicated nodes (typically for IoT gateways) or generic deployment nodes such as COTS hardware. Moreover, an autonomic manager is supposed to provide the adequate modules deployment policies thanks to logical effectors, on the basis of the information (QoS metrics, resource state, etc.) retrieved from the logical sensors. Let us precise here that the paper is not focused on the autonomic manager.

The contributions of this paper include (1) the design and the implementation of the QoS management modules, (2) the architecture allowing their integration in MW entities, and (3) their performance evaluation in terms of benefits and costs through an illustrative scenario coming from the vehicular transportation domain.

The remainder of this paper is organized as follows. Section II states the considered problem as well as the related state of the art. Section III presents the integration architecture of the QoS management modules into the oneM2M-compliant middleware entities. Section IV describes the design principles of these modules. Section V presents the performances emulation of our solution. Finally, Section VI concludes the paper and gives insights on our envisioned perspective works.

CONTRIBUTION POSITIONING AND RELATED WORK

As part of the standardization efforts, various MW-level service layers have been proposed in the context of the IoT. These MW layers include several functional and nonfunctional services for the management of IoT devices. However, these standard-based MWs do not propose any solution for the QoS management at the MW level. Indeed, QoS is considered a result of the underlying networks [1].

However, several specific (i.e. not standard) solutions [START_REF] Razzaque | Middleware for internet of things: a survey[END_REF] have been proposed. [4] proposes to enhance the MW WuKong [START_REF] Lin | Building Smart M2M Applications Using the WuKong Profile Framework[END_REF] for the QoS management. It introduces the concept of quality score that considers multiple QoS metrics (response time, reliability, etc.). Adequate physical devices are selected as well as their optimal deployment is decided in order to achieve the highest quality score. The limit of this approach lies in the fact that applications' QoS requirements are not taken into account dynamically. In the project MiLAN [START_REF] Heinzelman | Middleware to Support Sensor Network Applications[END_REF], Heinzelman proposes a MW that manages both nodes and the network. Depending on the application description and its expressed QoS requirements, the MW configures both the network and the MW nodes to meet these requirements. However, MiLAN needs a specific state diagram of every application scenario and for every WSN context, which is very complicated in the dynamically changing IoT context. Other solutions such as [START_REF] Sîrbu | A new platform for Human Computation and its application to the analysis of driving behaviour in response to traffic information[END_REF][8] rely on the integration of the MQTT protocol [START_REF] Banks | MQTT Version 3.1.1 Errata 01[END_REF] for QoS management. This protocol includes a basic form of QoS management. It offers three levels of message delivery guarantee: QoS Level 0: Messages are delivered in a best-effort fashion without receive acknowledgment; QoS Level 1: Messages are guaranteed to be delivered at least once; and QoS Level 2: Messages are guaranteed to be delivered exactly once. Let us also note that the last specification of the oneM2M standard [START_REF][END_REF] proposes to integrate the MQTT protocol. MQTT does offer a certain guarantee for message delivery. However, in the IoT context, applications can have different requirements additionally to the simple message delivery guarantee.

III. SOFTWARE ARCHITECTURE FOR A SEAMLESS INTEGRATION OF QOS MECHANISMS IN A ONEM2M-COMPLIANT MW

A. Seamless integration in the oneM2M-compliant OM2M MW The oneM2M standard is expected to prevail as the main IoT MW architecture since it enables and facilitates the interoperability at different levels (Fig. 3). At the communication level, the IoT entities are able to "talk" to each other, i.e. applications/objects are able to communicate with other applications/objects independently from their access network technologies or communications protocols. At the data level (i.e. semantic interoperability), entities are able to "understand" each other. This is achieved through the semantic extension, present in oneM2M since its release 2 [1]. The oneM2M functional architecture identifies logical entities dubbed "MW nodes" (typically server / gateways of previous Fig. 1), each one offering a portion of the MW service. It is a resource-oriented architecture (RoA) where the functionality of the system is exposed by means of APIs. Each of these entities is composed of software modules that implement each one of the node's features. Thus, based on this modular architecture of the MW node, we propose to integrate the new QoS-oriented mechanisms as modules. These modules can be incorporated dynamically at design or run time in a seamless fashion without any modification of the original MW node.

As shown in Fig. 4, the integration location of these QoS modules into the communication model of a oneM2M MW node, is justified by the constraint imposed by the different application level protocols (HTTP, CoAP, MQTT) supported by the node. Each of these application protocols has a different message (request or response) structure. We have chosen to propose our QoS modules in a protocol-agnostic way. Thus, new applications protocols are automatically supported as long as the MW node support them. This integration approach can be implanted in all opensource implementations of the oneM2M standard such as OCEAN Mobious [START_REF][END_REF], IoT-DM [12], or OASIS SI [START_REF]The IoT Oasis HomePage[END_REF], since they share the same modular architectural style. In the following section, we apply our approach to the open source Eclipse OM2M platform [START_REF] Alaya | OM2M : Extensible ETSI-compliant M2M Service Platform with Selfconfiguration Capability[END_REF], initially developed at LAAS-CNRS [15].

B. Application to Eclipse OM2M

OM2M nodes are built following a modular architectural style based on the OSGi standard [START_REF]The OSGi HomePage[END_REF]. Thanks to this implementation, it is possible to integrate our QoS mechanisms in the form of OSGi modules. Our integration approach is achieved so that the OM2M node maintains its modular design and can operates without these new modules (i.e. seamless integration). An OM2M node (in-cse or mn-cse) is composed of the following modules:

 Core module: The Core module is responsible of the processing of generic requests and responses (i.e. protocol-agnostic messages). It implements features such as Registration, Discovery, Re-routing, Notifications, etc.  Binding modules: The Binding modules act as translators of protocol specific messages to generic messages and vice versa. A binding module is necessary for every supported protocol (HTTP, CoAP, MQTT, etc.)  Persistence modules: The Persistence modules are responsible for implementing the data storage strategy.

There is on interface module, and as many as supported storage locations (in-memory, file or server databases)  Interworking Proxy Entity (IPE) modules: Similar to the Binding modules, they provide translation of generic messages into non-IP (Bluetooth, ZigBee, Z-Wave, etc.) messages and vice versa.

To achieve this integration, we had to consider two options: (1) to re-implement the Binding modules and Interworking Proxy Entity modules of a node in order to add a new interface to be used for the communication with our QoS modules. Such a modification would have resulted in a new version of Eclipse OM2M; or (2) to use the OSGi feature "Proxying Service" [START_REF]OSGi Core Release 6[END_REF] which allows to intermediate an OSGi service. We have chosen the second option which enables the integration of our mechanisms without affecting the oneM2M standard being implemented through Eclipse OM2M. Furthermore, this option has the advantage not to change any element of the current implementation of OM2M. As shown in Fig. 6, the main element of this architecture is the "adapter" module. This component is specified following a design pattern [START_REF] Gamma | Design Patterns Elements of Reusable Object-Oriented Software[END_REF]. It intermediates the OSGi service between the "core" module and the "binding" modules. Depending on its configuration (coming from the autonomic manager), it also decides to pass the request message through zero or several modules before reaching the "core" module. The same applies for the response message. An example is illustrated in Fig. 7.

IV. DESIGN PRINCIPLES OF THE QOS-ORIENTED MODULES

In this section, we present the design of our QoS-oriented modules that implement mechanisms inspired from QoS management at the IP level coming from IETF DiffServ working group [START_REF] Blake | An architecture for differentiated services[END_REF]. The DiffServ architecture is based on a simple model where traffic entering a network is first conditioned, then assigned to a class of behavior. Each class is uniquely identified by a code that can be found as a "mark" in the IP packets. The packets are then routed following the behavior associated to the code of the class to which they belong (e.g. packets marked A will be systematically delayed if the node load is higher that a given value). Following these same principles, five QoS modules acting on the applicative traffic (i.e. on the http requests/responses) have been designed and implemented in JAVA: The Adapter, the Classifier, the Dropper, the Delayer, and the Scheduler.

A. The Adapter

The algorithm of the Adapter module is inspired from [START_REF] Gamma | Design Patterns Elements of Reusable Object-Oriented Software[END_REF]. When a message is received by this module, the input policy is checked in order to pass the message into every module indicated in the input policy and in the specified order (lines 1 to 7). The input policy being applied, and if no module has dropped the message, it is passed to the "core" module for normal processing (line 8). The output policy is finally applied and similarly to the input policy (lines 9 to 17).

If any module drops the message (request as in line 5 or response as in line 14), an error message is issued and sent to the "binding" module for its transmission to the request issuer as specified by the oneM2M standard.

B. The Classifier

The Classifier module offers message classification and marking services. It first tries to identify the class of the received message (line 1). If a class is identified, the message is then marked with the associated tag (lines 2 and 5).

Algorithm 2: Classifier

C. The Dropper

The Dropper module offers a service of packet rejection following a given rejection percentage. Upon the reception of a message, the Dropper module first identifies the priority of the message which associated to its mark (line 1), then calculates the percentage of the previously rejected messages with the same priority (line 4). If this percentage is still lower than the specified one in the QoS policy, then the message is rejected and a null message is returned to the Adapter. Else, the message is returned without any modification to the Adapter (lines 5 to 8).

D. The Delayer

The Delayer module offers to delay messages based on their priority. It first identifies the priority of the message (line 1), and then waits the required delay corresponding to the identified priority (lines 3 to 6). After the elapsed delay, the message is returned without modification to the Adapter module.

E. The Scheduler

The Scheduler module redefines the message scheduling based on their priority. It operates through two processes: (1) the first process enqueues the received message in an internal queue, and delivers this message when it progresses to the head of the queue (lines 1 to 11), (2) the second process schedules (reorders) the messages within the queue according to their priority (lines [START_REF]The IoT Oasis HomePage[END_REF]

V. IMPLEMENTATION AND EVALUATION

The efficiency of the proposed approach is evaluated through a scenario (case study) dealing with the vehicular transportation area. Within this scenario, the first goal is to measure the expected benefits induced by a QoS policy consisting (to face a QoS degradation) in the dynamic deployment of several QoS modules on the considered MW entities. The second goal is to evaluate the cost associated to the performed deployment. The scenario is presented in the next section A. Section B and C are devoted to the evaluations associated to the two targeted goals.

A. Presentation of the scenario

We consider three Infrastructure-to-Vehicle (I2V) applications [START_REF]Vehicle Safety Communications Project Task 3 Final Report Identify Intelligent Vehicle Safety Applications Enabled by DSRC[END_REF] having different QoS requirements (see Table I). The considered architecture is shown in Fig. 8 and described through Table II. The applications are emulated through stochastic HTTP traffic injectors where 1500 requests are sent to the server and 1000 to the gateway, 500 requests from each application (A, B, and C). The MW level entities (server and gateway) are real entities whose specifications are provided in Table II. In order to assess the effects of the envisioned policies and implemented through the QoS modules, we have considered the processing time within the considered server and gateway MW nodes.

This scenario is divided into three stages:

1) Stage 1: Detection of an unsatisfied latency constraint and elaboration of a QoS-oriented global policy

The first stage is initiated by an event indicating to the autonomic manager that the latency constraint of application A (supposed to be more important than application A) is not satisfied. The autonomic manager is also notified that the average response times within the server and the gateway are respectively 65ms and 40ms, whatever the applicative traffic. In order to meet the 100ms of end-to-end latency required by the application A, still taking in account as best as possible the QoS requirement of applications B and C, we suppose that the autonomic manager decides to perform a global policy consisting in two successive (local) policies applied on the gateway then on the server (see stages 2 then stage 3). Let us recall here that our goal is not to discuss of the optimality of the chosen policy, but to evaluate the effectiveness of a plausible policy.

TABLE II. DESCRIPTION OF THE ARCHITECTURE SCENARIO

Managing Entity Element Description

Autonomic Manager

This entity implements the control loop MAPE-K Erreur ! Source du renvoi introuvable. and allows (among other tasks) to decide when, where and how to deploy the implemented modules in order to meet the QoS requirements of the targeted application(s).

Touchpoints Element Description

Sensors

A logical component allowing to retrieve the processing time in the different nodes of the middleware.

2) Stage 2: Implementation of a scheduling policy on the gateway (first part of the global policy)

The second stage consists in the implementation of the first part of the policy defined by the autonomic manager. This one has to deploy three different modules on the gateway: An Adapter, a Classifier and a Scheduler. This policy is aimed at prioritizing (on the gateway) the traffic coming from the application A (Fig. 9).

3) Stage 3: Implementation of a joint scheduling and dropping policy on the server (second part of the global policy)

The third stage consists in the implementation of the second part of the chosen policy, through the combination of a scheduling policy and a dropping policy within the server. Four modules have then to be deployed by the autonomic manager: An Adapter, a Classifier, a Scheduler, and a Dropper. This policy is aimed at prioritizing (on the server) the traffic coming from the applications A and B, and if the constraints is not satisfied, to drop the traffic coming from B (Fig. 10).

C. Evaluation of the costs associated to the QoS modules deployment 1) Introduction

Since we aim to dynamically handle QoS requirements of IoT applications, we need to take into account the deployment time of the QoS-oriented modules. The performance measurements presented hereinafter allows to assess the deployment time (including the activation time) of the QoS modules within the considered gateway and server MW nodes. In this test, and in order to not bias the results by additional upload time (linked to the network conditions), the QoS modules are supposed to be already present within the system hosting the MW node as illustrated in Fig. 13. The "Controller" entity depicted in Fig. 13 is responsible for the deployment of modules within the OSGi platform (and eventually remotely). The deployment of every module repeated over 1000 iterations and the results are presented and discussed in the following sections.

2) Results and Discusions Fig. 14 presents the average deployment time of each implemented QoS module. Among all the QoS modules, we see that the Adapter module has the highest deployment time (50ms), followed by the Scheduler (25ms), the Classifier (23ms) and finally the Delayer (18ms). Thus, the deployment time of a QoS policy is linked to the size of the involved QoS modules. Indeed, in our implementation, the size of the QoS modules are as follows: The Adapter module (i.e. OSGi Bundle) is 1Mb, the Scheduler is 12 Kb, the Classifier is 10kb, and finally the Dropper and the Delayer are both 7Kb. For example, overriding the scheduling policy will require around 100ms of deployment time.

Since the Adapter module is required for any QoS policy deployment, we could consider that the Adapter module has to be part of the initial deployment of the OM2M middleware node. Thus, only other QoS modules (that are small in size) are to be deployed during run-time depending on the QoS policy planned by the autonomic manager.

VI. CONCLUSION AND FUTURE WORK

QoS management in the IoT is still challenging goal. In this paper, we presented one of the approaches that we envision to meet IoT applications' QoS requirements. We detailed our vision of a modular architectures and how we can use them to manage the IoT applications' QoS requirements at the middleware level. We have also presented the design and implementation of QoS oriented modules, their integration architecture within the oneM2M-compliant OM2M middleware, and the experimental evaluation of both the benefits and costs of the proposed solutions through a scenario coming from the vehicular transportation domain.

Even though, the deployment of the QoS modules into the middleware nods can be considered, this solution cannot fit all the cases. Thus, we also consider, as future work, the dynamic deployment of microservices in which QoS management mechanisms will be implemented taking advantages of both approaches (joint deployment of QoS microservices and QoS modules).

Finally, the contributions presented in this paper fall in our general approach that consists in a dynamic and autonomous end-to-end management of the QoS at the middleware level through the deployment of QoS mechanisms within the middleware nodes (in the form of modules) or outside the MW (in the form of microservices).

Fig. 2 .

 2 Fig. 2. Overview of the deployment approach

Fig. 3 .

 3 Fig. 3. oneM2M's horizontal architecture (providing a unifying framework for silo applications)

Fig. 4 .

 4 Fig. 4. Integration of QoS management modules into the oneM2M communication model of a MW node

Fig. 5 .

 5 Fig. 5. Basic communication diagram of a oneM2M node before and after integration of QoS-oriented modules (QoS function)

Fig. 6 .

 6 Fig. 6. Internal structure of an OM2M node integrating QoS-oriented modules

Fig. 7 .

 7 Fig. 7. Adapter module of the proposed architecture

Fig. 8 .

 8 Fig. 8. Considered architecture for scenario

EffectorsAServer 10 Gateway

 10 logical component allowing to add/remove or modify modules into the middleware nodes. Entity that represents the set of instances of the infrastructure node specified in the oneM2M standard (i.e. IN-CSE) 1 1Entity that represents an intermediate middleware node as specified in the oneM2M standard (i.e. MN-CSE)

Fig. 9 .

 9 Fig. 9. Second stage of the scenario

Fig. 10 .Fig. 11 .

 1011 Fig. 10. Third stage of scenario

Fig. 12 .

 12 Fig. 12. Evolution of the processing time of traffics coming from applications A, B and C, within the server We can distinguish 5 phases:  Phase 1 [req# 1 to req# 264]: During this phase, the three traffics are handled without differentiation. We can notice an average of 65ms (for either A, B, or C). This will trigger the third stage of the scenario.  Phase 2 [req# 265 to req# 339]: The observed peak is related to the deployment of the QoS policy implemented by a new scheduling (i.e. Adapter + Classifier + Scheduler)  Phase 3 [req# 340 to req# 585]: This phase corresponds to the reduction and then the stabilization of the processing time for traffic A (36ms) and an increase of the processing time for traffic B and C (average around 80ms). Requirements of application A is thus satisfied. However, since application B is sensitive to delay (65ms + 80ms > 50ms), its requirements are no longer fulfilled. Therefore, the autonomic manager will augment the QoS policy in order to abandon all requests of application B if their waiting time (when leaving the Scheduler) exceeds 40ms.  Phase 4 [req# 586 to req# 660]: The observed peak in the processing time is related to the deployment of new elements to make evolve the already deployed QoS policy (i.e. deployment the Dropper module only).  Phase 5 [req# 661 to req# 1000]: This phase corresponds to the reduction and then the stabilization of the processing time for traffic A (15ms), traffic B (36ms but with 27% of dropped requests), and traffic C (30ms).

Fig. 13 .

 13 Fig. 13. Software architecture for the performance measurementsBased on this measured time, it is possible to estimate the total deployment time through this simple formula:

Fig. 14 .

 14 Fig. 14. Average deployment time (ms) of the QoS-oriented modules

Algorithm 1: Adapter

		Input: message; modules; input-policy; output-policy; CSEService.
		Output: message.
	00:	begin
	01:	for (i=0 to sizeof(input-policy)) then
	02:	id ← input-policy[i]
	03:	service ← module[id]
	04:	message ← service(message)
	05:	if (message==null) then
	06:	return error_message
	07:	end for
	08:	message ← CSEService(message)
	09:	for (i=0 to sizeof(output-policy)) then
	10:	id ← output-policy[i]
	11:	service
	12:	message ← service(message)
	13:	if (message==null) then
	14:	return error_message
	15:	end for
	16:	return message
	17:	end

  to 17)

	Algorithm 5: Scheduler
		Input: message; pattern.
		Output: message.
	00:	begin
	01:	Initialize p ←message priority;
	02: 03: 04: 05: 06: 06: 07: 08: 09: 10:	if (p ≠ null) then if (p is a key of pattern) then add message to queue wait for the message to be the head of the queue message ← head of the queue remove the head of the queue end if end if return message end
		Input: queue.
		Output: N/A
	00:	begin
	01:	while (true) then
	02:	if (queue is not empty) then
	03:	sort queue by priority
	04:	end if
	05:	end

TABLE I

 I

		.	CONSIDERED IOT APPLICATIONS
	App.	Description		Rate	Latency	Loss
	A [20] Traffic Signal Violation Warning	10 req/s (minimal)	100 ms (Allowable)	0% (Allowable)
	B [20]	Free-Flow Tolling	10 req/s	50 ms (Allowable)	N/A
	C [20] Just-In-Time Repair Notification 10 req/s	N/A	0% (Allowable)


Frédéric Zahm
email: frederic.zahm@irstea.fr

Adeline Alonso Ugaglia
email: adeline.ugaglia@agro-bordeaux.fr

Jean-Marc Barbier
email: jean-marc.barbier@supagro.inra.fr

Héloïse Boureau
email: heloise.boureau@bergerie-villarceaux.org

Bernard Del 'homme
email: bernard.delhomme@agro-bordeaux.fr

Mohamed Gafsi
email: mohamed.gafsi@educagri.fr

Pierre Gasselin
email: pierre.gasselin@supagro.inra.fr

Sydney Girard

Laurence Guichard
email: laurence.guichard@grignon.inra.fretchantal.loyce@grignon.inra.fr

Chantal Loyce

Bernard Del'homme E

Vincent Manneville
email: vincent.manneville@idele.fr

Amandine Menet
email: amandine.menet@educagri.fr

Barbara Redlingshöfer
email: barbara.redlingshofer@inra.fr

Evaluating sustainability of farms: introducing a new

Keywords: IDEA version 4, Sustainability assessment tools, Sustainable agriculture, Properties of sustainability, Farm sustainability indicators

come

Introduction

Recent states of the art looking at ways of assessing agricultural sustainability [START_REF] Schader | Scope and precision of sustainability assessment approaches to food systems[END_REF][START_REF] Lairez | Évaluer la durabilité en agriculture. Guide pour l'analyse multicritère des productions animales et végétales[END_REF][START_REF] De Olde | Assessing sustainability at farm-level: Lessons learned from a comparison of tools in practice[END_REF] have identified a whole plethora of different tools and methods, including a great variety of criteria and indicators. At the heart of this diversity are a number of vastly different conceptual frameworks. Establishing such a framework is, of course, a vital first step in any analysis of farming sustainability. A conceptual framework relating to farming sustainability has four main objectives: (1) to present the general objectives of the method in question; (2) to discuss the theoretical literature and underlying visions of the authors relating to sustainability [START_REF] Hansen | Is agricultural sustainability a useful concept?[END_REF][START_REF] Pope | Conceptualising sustainability assessment[END_REF][START_REF] López-Ridaura | Evaluating the sustainability of complex socioenvironmental systems. The MESMIS framework[END_REF][START_REF] Kates | What is sustainable development[END_REF]; (3) to characterise the farming system being studied (plot, cropping system, entire farm, region, country, etc.) and identify its relationships with other meta-systems [START_REF] Smith | Assessing the sustainability of agriculture at the planning stage[END_REF][START_REF] López-Ridaura | Multiscale methodological framework to derive criteria and indicators for sustainability evaluation of peasant natural resource management systems[END_REF] and (4) to lay down the procedures to be used (the operationnel process and also interactions between disciplines, stakeholders' participation, methods to select and aggregate indicators…). The IDEA method (Indicateurs de Durabilité d'une Exploitation Agricole or Farm Sustainability Indicators) is an indicator-based approach to analyze and assess the level of sustainability of a farm. First developed in the late 1990s, it has been updated on two occasions (Vilain et al., 2008;Zahm et al.;2008). In this article, we present the latest conceptual framework developed based on work carried out by the IDEA Scientific Committee. The originality of this framework lies in the combined use of two theoretical approaches to analyse agricultural sustainability and to assess the sustainability of a farm.

The first part of the paper is a state of the art of the two possible theoretical approaches to assessing sustainability. The second part shows how the development of the IDEA v.4 conceptual framework has allowed the authors to make the following main advances based on this review of literature. Firstly it has been established a new theoretical framework based on five properties of sustainability (Ability to produce and reproduce goods and services; Autonomy; Robustness, Territorial embeddedness and Overall responsibility) and twelve goals (see table 1) taking into account also five new societal goals compared to IDEA version 3 (food, circular economy, climate change, air quality and low use of resources). Secondly, this new conceptual framework led to the proposal of 53 indicators structured / organized according to a double evaluative approach (and also two assesment grids): a first approach based on the three dimensions of sustainable development to assess the three agro-ecological, socio-territorial and economic dimensions of a sustainable farm, and second approach (new in this version) to qualify the degree of sustainability of a farm for each of the five properties. The third part of the paper highlights the possible uses and future developments of IDEA v.4 and explains the key theoretical contributions made by this research.

Two types of indicator-based approaches to assess agricultural sustainability

The following literature review identifies two indicator-based conceptual frameworks [START_REF] Binder | Considering the normative, systemic and procedural dimensions in indicator-based sustainability assessments in agriculture[END_REF] to analyse agricultural sustainability. The first uses an goal-focused approach, while the second is based on key properties of sustainability.

An assessment approach based on agricultural sustainability goals

An objective-based, or "goal-oriented conceptual approach" (Von Wirén-Lehr, 2001) views agricultural sustainability as "the ability to satisfy a set of goals" [START_REF] Hansen | Is agricultural sustainability a useful concept?[END_REF]. In other words, sustainable agriculture is defined by the goals it aims to achieve [START_REF] Kates | What is sustainable development[END_REF]. Viewing sustainability in this way is connected both to the societal issues faced by farmers and farming in general (global sustainability) and the internal goals which farmers aim to achieve (internal sustainability). This can be defined as the normative dimension of sustainability, or "a discussion of issues for which a consensus has been reached and a prioritisation of different actions needing to be taken" [START_REF] Godard | Le développement durable et la recherche scientifique à l'INRA[END_REF]. It points farmers in the right direction to achieve sustainability, based on pre-defined objectives (Sala et al., 2015). This approach depends on society's values, and the perception of sustainability is framed by what society is aiming to achieve [START_REF] Waheed | Linkage-based frameworks for sustainability assessment: making a case for driving force-pressure-state-exposure-effect-action (DPSEEA) frameworks[END_REF].

The literature review leads to the following conclusions: 1) the term "goals" does not appear uniformly throughout the literature. It is often replaced by other terms such as "objective", "issues", "challenges", "themes", and "priorities"; 2) the term is based on a normative representation of sustainable development through its three official dimensions (environmental, social and economic), [START_REF] Unced | Endorsed at the United Nations Conference on Environment and Development[END_REF]. Such a normative approach of sustainable development was confirmed in 2015 by the United Nations with the adoption of the 2030 program for sustainable development. The program includes seventeen Sustainable Development Goals, including Goal 2 -"[...] Promoting Sustainable Agriculture" (UNO, 2015), which specifically addresses the goals of a sustainable agriculture.

An assessment approach based on properties of agricultural sustainability

The second approach to assessing agricultural sustainability focuses on properties (also referred to as "attributes" or "principles"). This "system-based framework" [START_REF] Van Cauwenbergh | SAFE-A hierarchical framework for assessing the sustainability of agricultural systems[END_REF] or Systembased Property Oriented indicator Framework (SPOF) (Bockstaller et al., 2007), aims to create a set of indicators based on their ability to clearly identify the status of a system based on the properties of sustainability [START_REF] Altieri | L'agroécologie: bases scientifiques d'une agriculture alternative[END_REF][START_REF] Conway | The Properties of Agroecosystems[END_REF][START_REF] Smyth | FESLM: An International Framework for Evaluating Sustainable Land Management[END_REF][START_REF] Bossel | Indicators for sustainable development: theory, method, applications[END_REF][START_REF] López-Ridaura | Multiscale methodological framework to derive criteria and indicators for sustainability evaluation of peasant natural resource management systems[END_REF]. For [START_REF] Hansen | Is agricultural sustainability a useful concept?[END_REF] sustainability "interpreted as a property of agriculture has been developed in response to concerns about threats to agriculture, with the goal of using it as a criterion for guiding agriculture as it responds to change".

Such an approach based on the qualification of sustainable development had already been proposed by [START_REF] Rousselet | Durabilité des exploitations agricoles et méthode IDEA. Analyse de l'utilisation et de la perception de la méthode[END_REF] in his work on ecodevelopment. He retained three of them: the notion of self-reliance the (autonomy of decisions and the emergence of alternative modes of development taking into account the historical contexts of each country), (ii) a fair management of the essential needs of each (material or immaterial) and (iii) ecological prudence. This approach was also used in the MESMIS research program [START_REF] López-Ridaura | Evaluating the sustainability of complex socioenvironmental systems. The MESMIS framework[END_REF][START_REF] Astier | Sustainability indicators, alternative strategies and trade-offs in peasant agroecosystems: analysing 15 case studies from Latin America[END_REF], which identified seven key properties to analyse rural agricultural sustainability in Latin America: productivity, stability, reliability, resilience, adaptability, equity and autonomy. [START_REF] Bossel | Indicators for sustainable development: theory, method, applications[END_REF] uses a similar approach, referring to "fundamental properties" to define the "internal viability of the system being studied" and the "contribution made by the system to the performance of other systems". He measures a system's contribution to sustainable development by the presence of six properties: existence, effectiveness, freedom, security, adaptability and coexistence.

Comparative summary of the two approaches

The advantage of a goal-driven approach is that it facilitates communication between scientists and stakeholders (Sala et al., 2015). In this case, farmers and stakeholders who have to implement changes can easily pinpoint the real actions they need to take in order to achieve their particular goals [START_REF] Alkan-Olsson | A goal oriented indicator framework to support integrated assessment of new policies for agri-environmental systems[END_REF]. However, one of the downsides of this approach is that it can generate unnecessarily long lists of indicators if not combined with a systemic analysis of the farm being studied [START_REF] Alkan-Olsson | A goal oriented indicator framework to support integrated assessment of new policies for agri-environmental systems[END_REF]. There is also the risk that the choice of goals may be too subjective, because of the likelihood that those laying down the goals may allow themselves to be influenced by their own personal values [START_REF] Hansen | Is agricultural sustainability a useful concept?[END_REF]. It is more likely to appear in the case for the external sustainability.

Concerning the property-based approach, the advantage is that it remains generic and unaffected by the local context [START_REF] Alkan-Olsson | A goal oriented indicator framework to support integrated assessment of new policies for agri-environmental systems[END_REF]. That said, some authors, such as Bockstaller et al. (2007) have noted that such an approach can be awkward to use in practice, because it takes considerable time to explain it to people who are unfamiliar with such methods.

There is also a difference of point of views, goals-based framework include natively the ability to engage changes while property oriented approaches are more static.

Version 4 of the IDEA conceptual framework

IDEA version 4 method is an indicator-based sustainability assessment tool [START_REF] Binder | Considering the normative, systemic and procedural dimensions in indicator-based sustainability assessments in agriculture[END_REF]. It aims to evaluate the sustainability of a farm. It has been developed with two objectives in mind. The first objective is to be used as an educational and transparent tool to teach students in an operational way the concept of agricultural sustainability and farm sustainability. The second objective is to be used as a monitoring or decision support tool for farmers but also advisors to support the transition toward a more sustainable agriculture.

IDEA version 4 is based on the (overall) conceptual framework developed and presented on figure 1. This conceptual framework formalises both (i) the theoretical framework and (ii) the operational process of the IDEA version 4 method.

The theoretical framework

As the literature review shows, a conceptual framework based solely on normative goals of sustainability (as shown in IDEA version 3: [START_REF] Vilain | La méthode IDEA Indicateurs de durabilité des exploitations agricoles, 3ème édition[END_REF][START_REF] Zahm | Farm Sustainability Assessment using the IDEA Method. From the concept of farm sustainability to case studies on French farms[END_REF] is necessary to give first farmers but also all other stakeholders a clear sense of the goals to be achieved. While version 4 does not abandon this approach, it (the approach) does not allow a clear identification of the status of a system in terms of properties of sustainability. For this reason, IDEA v.4 also includes a property-based approach. The advantage is that it does not rely on societal goals, which depend on the local area they are embedded in.

Selecting indicators from a theoretical assessment framework based on properties of agricultural sustainability has the advantage of not giving more weight and attention to the goals that would be contingent of the local scale (territory). This new approach adopted in Version 4 of IDEA method is therefore more generic than the IDEA method (version 3) which was based on a conceptual goals sustainability framework [START_REF] Zahm | Farm Sustainability Assessment using the IDEA Method. From the concept of farm sustainability to case studies on French farms[END_REF].

In theoretical terms, the IDEA conceptual framework is one of strong sustainability: i.e. it does not subscribe to the principle that generated capital can ever compensate for the loss of natural capital [START_REF] Daly | Towards some operational Principles of Sustainable Development[END_REF]. It is based on double vision of sustainable agriculture and sustainable farms as defined in box 1.

Box 1: Agricultural and farming sustainability concepts as employed in IDEA v.4

Sustainable agriculture is a form of agriculture that is economically viable, environmentally friendly, humane, and socially fair. It contributes both to the overall sustainability of the local area in which it is practised, and to the achievement of global sustainable development goals. A sustainable farm is viable, acceptable, easily transmissible and readily reproducible. It is founded on a socially responsible approach. This approach depends on the choices made by farmers relating to the effects of their production methods on the quality of life of those living in the local area, as well as their contribution to realising global goals, such as fighting climate change, air quality, food safety, etc. Source : [START_REF] Zahm | Agriculture et exploitation agricole durables : état de l'art et proposition de définitions revisitées à l'aune des valeurs, des propriétés et des frontières de la durabilité en agriculture[END_REF] To qualify the sustainability of a farm, we defined five key properties [START_REF] Zahm | Agriculture et exploitation agricole durables : état de l'art et proposition de définitions revisitées à l'aune des valeurs, des propriétés et des frontières de la durabilité en agriculture[END_REF] based on the state of the art detailed above. The Capacity to produce and reproduce goods and services (property 1) refers to a farm's long-term ability to efficiently produce and reproduce goods and services, without eroding the natural and social resources it possesses. Autonomy (property no. 2) covers a farm's ability to produce goods and services from its own resources (inputs, human resources, and other production factors). It also includes its freedom to make decisions, its capacity to develop independently, and the extent of its dependence on public instruments (financial support, quotas, subsidies, etc). Robustness (property no. 3) is a farm's ability to adapt to environmental, social, and economic fluctuations, and to deal with new conditions and/or disruption and external shocks. This property encompasses the concepts of resilience, adaptation, and flexibility. The Territorial embeddedness (property 4) means the ability of a farm to contribute to the co-production of local resources. It also highlights the nature and extent of market and non-market connections created with the local area, local residents, and stakeholders. Global responsibility (property no. 5) refers to the extent of a farm's commitment to a global approach, taking into account the environmental and social consequences of their mode of operation. This commitment is grounded in values of ethics and equity. As with territorial influence, this property does not focus exclusively on the farm itself, but also examines the impact of its actions at higher levels of organisation.

The new conceptual framework also makes use of two concepts of sustainable agriculture. First, the restricted sustainability or farm-focused sustainability defined as being sustainable by and for itself through the use of sustainable practices. This restricted sustainability is "similar to the concept of durability which designates the capacity of the system to maintain itself but is economically and socially limited" [START_REF] Terrier | Assessing the sustainability of activity systems to support households' farming projects[END_REF]. Secondly, the extended sustainability aims to identify the societal goals of farms which also contribute to sustainable development at a larger scale (local, national and global) [START_REF] Godard | Le développement durable et la recherche scientifique à l'INRA[END_REF][START_REF] Terrier | Assessing the sustainability of activity systems to support households' farming projects[END_REF].

Twelve goals were selected on the basis of a literature review and also taking into account the goals set in the IDEA version 3 method but enriched by new societal goals (food safety and sovereignty, territorial development in relation with circular economy, climate change, air quality and low use of resources) within this version 4. These twelve goals may be divided according to these two sustainability levels of sustainability analysis (extended and restricted sustainability), as shown in the table 1. The six goals refering mainly to local and global environment of the farm are assigned to extended sustainability (1.

Preserve natural resources (biodiversity, soil, water, air); 2. Preserve non-renewable resources: 3.

Preserve and/or develop landscapes ; 4. Deal with the challenge of climate change (through mitigation and adaptation); 5. Contribute to food safety and sovereignty ; 6. Contribute to employment and territorial development). The six goals referring mainly to the farm level (including the farmer, his family and employees) are grouped into restricted sustainability (7. Ensure the economic viability and long-term survival of the farm ; 8. Contribute to quality of life ; 9. Maintain independence and freedom to act ; 10. Make ethically responsible commitments; 11. Generate and share knowledge and know-how ; 12. Ensure the health and wellbeing of livestock).

Table 1 : the twelve goals relative to their level of sustainability for a farm

Operational process

The operation application of the IDEA v.4 conceptual framework is founded on three key elements. The first is the definition and creation of indicators based on three principles: (i) compatibility with the relevant theoretical framework, (ii) ensuring good quality indicators, based on recognised standards (Reeds et al., 2006) (relevance, principle of parsimony, sound scientific grounding, fair assessment, measurability, educational value, transparency, and ease of interpretation based on benchmark thresholds), and (iii) ease of use for farmers, advisors, and students. The second element is the creation of a heuristic chart based on the five key properties of sustainability (Figure 2), leading to the design of 53 indicators. The third and final part of the operational process is the construction of two complementary grids of assessment, as shown below (figures 3 and 4). These two assessments use the same 53 indicators in two ways: one assessment grid organized according to the five properties of sustainability, and another one based on a normative approach relative to the three dimensions of sustainable agriculture. The main calculation rules can be described as follows.

The higher the score (between 0 and 100), the more sustainable the farm is. There is a final sustainability score for each of the three dimensions (see example in figures 3 and 4) with an equal weight between the 3 dimensions (see table 2). The final sustainability level of the farm is the lowest score out of all three dimensions, bearing in mind that the method is based on the principle of "strong" sustainability (e.g. a score of 58/100 for example for a farm, see Figure 3). 2) and there is a ceiling value of units for each component (between 20 units to 35 units depending the different components). This scores (or units) system is based with an upper limit for each indicator. Maximum scores are set for each indicator in order to set an upper limit on the total number of sustainability units for each component and dimension (100 units). The maximum score awarded to each indicator is defined not with the aim of establishing an absolute optimal value, but rather practices, behaviour or levels of results that do not give rise to fundamental problems concerning the notion of sustainability for the component. The sum of the durability units of the indicators within each component is higher than the ceiling value of the component. This limitation weights the relative weight of the number of indicators per component and allows a large number of combinations to reach the maximum level of durability of the component. This cap system is established to avoid the process of offsetting or overweighting one or more indicators. From experience following the many tests (more than 3000 farms) of use of the three previous versions of the IDEA method [START_REF] Zahm | Farm Sustainability Assessment using the IDEA Method. From the concept of farm sustainability to case studies on French farms[END_REF], Vilain et al., 2008;[START_REF] Rousselet | Durabilité des exploitations agricoles et méthode IDEA. Analyse de l'utilisation et de la perception de la méthode[END_REF] by applying a such system of ceiling to each component, the sustainability of many different farms can be assessed, taking into account the fact that they cannot all be covered by a single socio-technical model. Because of the vast range of local contexts and production systems in which farms operate, each will use a different combination of actions and take its own path to achieving sustainability. By displaying the information in this way, farmers can see areas where there is still progress to be made. An example of this aggregation process is shown in figure 4 below. It concerns a farm with a score of 94 sustainability units for the agroecological dimension, 89 units for the socio-territorial dimension and 58 units for the economic dimension.

Figure 4 : example of assessment evaluation based on three dimensions and a further 13 components for a farm

The evaluation structured according to the five key properties of sustainability

In this approach, the fifty-three indicators are structured around our five key properties (Capacity to produce and reproduce goods and services, Autonomy, Robustness, Territorial embeddedness and Global responsibility), which are themselves divided up into fourteen different branches (from limiting exposure to hazards to Committing on a local and institutional level, see Figure 5). One of the key strategic choices made was not to aggregate the scores of each of the five properties into an overall sustainability score.

They are aggregated only within each property. The reason why they are aggregated in this way is that a more "overall" style of aggregation does not adequately identify potential actions to be taken for each individual property. By looking at them individually, it is possible to work with farmers to improve the areas of their operation identified as being the least sustainable. The second methodological choice was to include an ascending system of aggregation, working up through the different intermediate nodes of the 14 branches making up each property, as show in Figures 2 and5).

The third strategic choice was to use hierarchical qualitative aggregation, making use of the DEXi multicriteria decision application [START_REF] Bohanec | A qualitative multi-attribute model for economic and ecological assessment of genetically modified crops[END_REF]. This application assigns qualitative classes of sustainability (e.g. low, medium, high) to each indicator. After the aggregation process based on utility functions, results are displayed for all the nodes, as shown in the diagram in figure 5. These twelve indicators are then aggregated according to the "sub-branches" of each category to evaluate the extent to which that category has been achieved (the capacity to produce and reproduce goods and services in this case).

Discussion

The new IDEA v.4 conceptual framework was developed based on the following objectives: (1) ensuring it remained a useful teaching aid while introducing a new theoretical approach based on properties of sustainability, (ii) maintaining its scientific credibility by including new scientific knowledge gained since the last version 3, (iii) maintaining the key operational features recognised by the existing user base. A number of new societal issues have also been included: food, the circular economy, climate change, air quality, and restraint (low) in use of resources.

Finally, these two assessment grids are complementary. There is no hierarchy between them. Each shows in a different way the concept of a sustainable farm. While the two complementary approaches used in the IDEA v.4 have now been finalised, both in terms of the conceptual framework and their indicators (components/dimensions and branches/properties), there is still work to be done on their practical application.

For the three-dimension approach, the assessment grids have now been completed (see table 2 and appendice 1), and a working system has been developed to automatically input data and generate the two diagrams, as shown in Figures 3 and4. This works through Microsoft Excel. A number of modifications and improvements were made to this approach following a trial period from 2015 to 2017, where 61 farming systems were studied, ranging from livestock breeding and crop-livestock, to arable crops (used for the dimensions) and viticulture (used specifically for the economic dimension). These sites are characterised by very different soil and climate types (Nouvelle Aquitaine, Brittany, Midi-Pyrénées, and Rhône-Alpes) and varied collective and individual dynamics. First tests show that IDEA version can be used as a self-assessment diagnosis tool directly by farmers.

For the five-property approach, the decision rules for aggregating the indicators will be finalised as part of the ACTION research program (CASDAR 2017-2021) and will make use of the contingency matrix contained within the DEXi application.

Our first operational tests have shown that the "properties" and "dimensions" methods complement each other well when used together, providing a clear training tool to teach agricultural sustainability, as well as a fast and efficient way to display the overall sustainability of a farm (via qualitative analysis of the property branches) without having to collect all data from each indicator.

The next key task will be to finalise a clear, operational aggregation table. It would also be interesting to look at whether this generic analytical framework could be applied to farming systems outside of Europe. It would also be interesting to examine possible uses of IDEA v.4 within the process of advising agroecological transition.

Conclusion

This new conceptual framework makes the following contributions to the field: (i) an explanation of the notion of "properties" within a farming system and an integrated understanding of the complexities of such systems, as suggested by Lopez-Ridaura et al.(2002), (ii) a reference for a transparent normative evaluation system for farms, based on twelve objectives divided up according to their relevant theoretical frameworks (extended and restricted sustainability) and (iii) a way of evaluating a farm's sustainability through two modes of interpretation: the first through the three dimensions of sustainable development, and the second through the properties attributed to a sustainable farming system.

The next research goals will be to work with stakeholders to examine the extent to which IDEA's twin dimension/property can be used to support agro-ecological transition for farmers and advisers, particularly in identifying levers for actions. The French CASDAR ACTION research project will look specifically at these issues.

Examples of calculation for two indicators of Socio-territorial dimension (B)

The

Figure 1 :

 1 Figure 1: the overall conceptual framework of the method IDEA version 4

Figure 2 :

 2 Figure 2 : heuristic chart showing the five properties of a sustainable farm developed by the method IDEA version 4

Figure 3 :

 3 Figure 3 : First grid assessment based on three sustainability dimensions

  Within each dimension, indicators are aggregated by component. These components each have three functions: (1) theme-based organisation of the 53 selected indicators (table 2), (2) weighting each component within each dimension, and (3) compensating sustainability of the indicators contained within one component. The dimension score is the cumulative number of basic sustainability units for the different indicators in the scale after weighting and aggregating the individual indicator scores within each component. Each dimension scale goes from 0 to 100 units of sustainability (table

Figure 5 :

 5 Figure 5 : Second assessment grid based on the five properties of agricultural sustainability

  of direct selling or short supply chains 2 units max No direct selling or no Short Supply Chains 0 Direct selling or short supply chains < 5% of the turnover: 0 Direct selling or short supply chains < 50 % of the turnover: 1 Direct selling or short supply chains > 50 % of the turnover: 2 Item 2: Development of geographic proximity…………….3 units max Proximity sale to the final consumer or local food network: -In a collective way …...... 3 units -Individual way ……………2 units Item 3: To contract with local canteens or local catering or local public markets………… ………………………………………………….3 units max 5 Goals 5. Contribute to food safety and sovereignty 6. Contribute to employment and territorial development 7. Ensure the economic viability and long-term survival of the farm 9. Maintain independence and freedom to act and satisfaction at work ………..4 units max Self-assessment by the farmer on a scale from 0 to 4 Item 2: Mental workload in the time ………………………3 Number of weeks per year when the farmer feels overworked: -Over 8 weeks …………………0 unit -From 4 to 8 weeks ………….. 1 -From 1 to 3 weeks ………….. 2 -Less than one week ………….3 units Item 3: Time off …………………….…………………..3 units max Question 1: Essentially, do you think it is necessary to take time off ? Question 2 : Do you take it ? if answer is yes to both questions …… 3 units if answer is no to both questions …. 0 unit -Yes / no …………. -3 units Item 4: Arduousness Self-assessment on a scale from 0 to -4 (very hard work) 6 Goals 7. Ensure the economic viability and long-term survival of the farm 8. Contribute to quality of life Property Global responsibility

Table 2 :

 2 IDEA assessment grid (version 4) showing the three sustainability dimensions of a farm with its 13 components of sustainability, 53 indicators and associated scores

th European IFSA Symposium, 1-5 July 2018, Chania (Greece)

Appendice 1 : Four examples of indicator calculation

Example of calculation for an indicator of Agro-ecological dimension (A)

The indicator A 18 : Reducing impact of production on climate change


Shuman Jia

Nicolas Duchateau

Pamela Moceri

Maxime Sermesant

Xavier Pennec

Parallel Transport of Surface Deformations from Pole Ladder to Symmetrical Extension

come   L'archive ouverte pluridisciplinaire

Introduction

Analyzing cardiac function, notably myocardial deformation along cardiac cycle, can reveal subtle changes underlying disease development, and therefore improve risk stratification for patients. However, temporal deformations (cyclical or longitudinal) are complex due to subject-specific anatomy. Normalization of these trajectories into a common reference frame is an essential prerequisite in statistical analysis [START_REF] Duchateau | A spatiotemporal statistical atlas of motion for the quantification of abnormal myocardial tissue velocities[END_REF][START_REF] Bai | A bi-ventricular cardiac atlas built from 1000+ high resolution mr images of healthy subjects and an analysis of shape and motion[END_REF].

Nevertheless, it is a challenging task to construct a robust method for the normalization of temporal deformations, both theoretically and numerically. In cardiac imaging, the first step often includes segmenting the region of interest from the images, which generates its surface or volume as results. Then, to model the deformation between two shapes, depending on properties of the shapes, different non-rigid registration algorithms may be suitable in specific scenario. We choose to place our method in a space of diffeomorphic transformations. In particular, diffeomorphism provides invertible and folding-free registration results, which enables a symmetric encoding of deformation trajectories.

Given that diffeomorphisms are parameterized via flow of velocity fields, here stationary velocity field (SVF) [START_REF] Vercauteren | Symmetric log-domain diffeomorphic registration: A demons-based approach[END_REF], their normalization requires vector-based transport. In differential geometry, parallel transport specifies how to realize an infinitesimal transformation (a tangent vector) along a curve from one point to another of a manifold, as illustrated in Fig. 1(a). The concept was introduced in medical imaging by [START_REF] Younes | Jacobi fields in groups of diffeomorphisms and applications[END_REF] and used for neuroimaging studies in [START_REF] Qiu | Parallel transport in diffeomorphisms distinguishes the time-dependent pattern of hippocampal surface deformation due to healthy aging and the dementia of the alzheimer's type[END_REF]. To apply it to cardiac sequences, we need to:

-Parameterize the temporal deformations Φ ti from the subject-specific shape S at baseline to its shape S ti at time t i by SVF v ti ; this step amounts to computing the logarithm of the deformations such that Φ ti = exp(v ti ), or to register S to S ti . -Transfer these SVFs along the inter-subject deformation geodesic Φ S from the space of S to a common geometry T , often called a template.

These steps lead to a representation of all the subject-specific deformations as infinitesimal deformations of the same anatomy. We can thus perform proper population comparison in terms of shape evolution along the cardiac cycle, as shown in Fig. 1(b). Despite the fact that the definition of logarithm may be well developed in theory, implementations of its computation could be unstable due to numerical inconsistency. While computing registration/geodesics, the logarithms of surface deformations are only sparsely defined in the space (on the shape), which differs from image deformations. Careful numerical implementation of parallel transport algorithm is also needed.

Parallel transport methods in medical image analysis are currently based on ladders (like Schild's and pole ladders [START_REF] Lorenzi | Schilds ladder for the parallel transport of deformations in time series of images[END_REF][START_REF] Lorenzi | Efficient parallel transport of deformations in time series of images: from schilds to pole ladder[END_REF]) or on variations of Jacobi Fields [START_REF] Younes | Jacobi fields in groups of diffeomorphisms and applications[END_REF][START_REF] Louis | Parallel transport in shape analysis: a scalable numerical scheme[END_REF]. These methods are first order approximation schemes which need to be Algorithm 1 Pole ladder transport of the vector u along the geodesic [S, T ] -Compute the midpoint M = exp S ( 1 2 log S (T )) on the intersubject geodesic; -Compute the geodesic form the endpoint S = exp S (u) of the temporal geodesic segment to the midpoint M , and shoot twice to get the inverse endpoint: T = exp S (2 log S (M )); -Return the vector trans(u) = -log T (T ) and then apply it to T : T = exp T (trans(u)).

iterated along the curve. In contrast, pole ladder was recently discovered to be of third order in general affine connection spaces [START_REF] Pennec | Parallel transport with pole ladder: a third order scheme in affine connection spaces which is exact in affine symmetric spaces[END_REF], which makes it a very attractive method to implement. In order to further improve the symmetry and thus the numerical stability with respect to the implementation of [START_REF] Lorenzi | Efficient parallel transport of deformations in time series of images: from schilds to pole ladder[END_REF], our method relies on the definition of middle point and geodesic symmetry.

Methodology

Pole Ladder

Pole ladder is based on using the curve as the diagonal of the geodesic parallelogram to realize parallel transport (see Fig 2 and Algo. 1). Let u be the initial tangent vector to the geodesic segment that encodes the temporal deformation exp S (tu) (t ∈ [0, 1]). Originally, pole ladder computes a midpoint on the geodesic [S, T ] and expands twice the geodesic form the endpoint S to the midpoint to obtain the point T . In this paper, we propose to reformulate the doubling of the geodesics with a mid-point geodesic symmetry (Algo. 2). The mid-point M of a geodesic segment [S, T ] is defined as M = γ [S,T ] ( 12 ). The mappings from M towards the two sides meet the definition of a geodesic symmetry:

γ [M,S] (t) = -γ [M,T ] (t).
Although this novel version of pole ladder is theoretically equivalent to the previous one, it is numerically more stable in our experiments. This may be emphasized by the fact that in medical imaging we are encoding tangent vectors with infinitesimal deformations and that changing the object which is deformed may have a drastic numerical impact.

Numerical Accuracy

Recent mathematical developments have enabled the numerical analysis of pole ladder in affine connection spaces with symmetric connections [START_REF] Pennec | Parallel transport with pole ladder: a third order scheme in affine connection spaces which is exact in affine symmetric spaces[END_REF]. In Lie groups, the Baker-Campbell-Hausdorff (BCH) formula provides an expansion of the composition of two group exponentials in the Lie algebra: BCH(v, u) = log(exp(v) • exp(u)). This formula has been thoroughly used in registration algorithms [START_REF] Bossa | Contributions to 3d diffeomorphic atlas estimation: application to brain images[END_REF]. In general affine connection manifolds, a somewhat similar formula can be established based on the curvature instead of the Lie bracket [START_REF] Gavrilov | Algebraic properties of covariant derivative and composition of exponential maps[END_REF]. The double exponential exp x (v, u) = exp y (Π y x u) corresponds to a first geodesic shooting from the point x along the vector v, followed by a second geodesic shooting from y = exp x (v) along the parallel transport Π y x u of the vector u. [START_REF] Gavrilov | Algebraic properties of covariant derivative and composition of exponential maps[END_REF] has shown that the Taylor expansion of the log of this endpoint h x (v, u) = log x (exp x (v, u)) is:

h x (v, u) =v + u + 1 6 R(u, v)v + 1 3 R(v, u)u + 1 12 ∇ v R(u, v)v + 1 24 (∇ u R)(u, v)v + 5 24 (∇ v R)(u, v)u + 1 12 (∇ u R)(u, v)u + O( u + v 5 ).
When applied to our reformulation of pole ladder using geodesic symmetry, we find that the error on one step of pole ladder to transport the vector u along a geodesic segment of tangent vector [S, T ] = [exp M (-v), exp M (v)] (all quantities being parallel translated at the mid-point M ) is:

Π M T trans(u)-Π M S u = 1 12 ((∇ v R)(u, v)(5u -2v) + (∇ u R)(u, v)(v -2u))+O( v+u 5 ).
We see here that one single step of pole ladder is of order three, thus much more accurate than the other first order parallel transport schemes. Moreover, the fourth order error term vanishes in affine symmetric spaces since the curvature is covariantly constant in these spaces. In fact, one can actually prove that all error terms vanish in a convex normal neighborhood of an affine connection space: one step of pole ladder realizes an exact parallel transport (provided that geodesics and mid-points are computed exactly of course) [START_REF] Pennec | Parallel transport with pole ladder: a third order scheme in affine connection spaces which is exact in affine symmetric spaces[END_REF]. This result makes pole ladder a very attractive scheme. In particular, Lie groups have a canonical symmetric space structure thanks to the symmetry s g (h) = gh -1 g for any elements g, h of the Lie group. This is an affine structure which is generally not metric. The symmetry generates a canonical connection which is exactly the symmetric Cartan-Schouten connection. Since the geodesics of this connection going through identity are parameterized the flow of SVFs, we can conclude that pole ladder on SVFs is exact, at least theoretically.

SVF-Based Transport

In practice, we consider sparse point-to-point correspondences between two shapes (established here with the commercial speckle-tracking software) to compute diffeomorphic transformation. Thus, here the solution for the log is not unique and needs to be spatially regularized. Following [START_REF] Rohé | Svf-net: Learning deformable image registration using shape matching[END_REF], the sparse displacement field on the mesh vertices is interpolated to a dense image grid using with a standard thin-plate spline (TPS) kernel (stiffness of zero) [START_REF] Davis | A physics-based coordinate transformation for 3-d image matching[END_REF]. The TPS fits the smooth surfaces and resistance in myocardial contraction. Then, a symmetric iterative procedure computes explicitly a SVF from the displacement field using BCH formula. The result gives a smooth SVF that linearly extends outside the grid borders.

The SVFs for temporal and intrasubject transformations are then used to compute the transported SVF to the template space using our symmetric pole ladder transport. In this context, we hypothesize that cardiac shape variations and temporal deformations can be efficiently modeled in a space of diffeomorphic transformations. The detailed shape variability that is lost during registration process will be transported. That is the reason why we report fiducial localisation error due to shape registration in Sec 3.

Benchmark Transport Algorithm

Simple transport, conjugate action, which has been tested for cardiac motion analysis [START_REF] Duchateau | A spatiotemporal statistical atlas of motion for the quantification of abnormal myocardial tissue velocities[END_REF][START_REF] Bai | A bi-ventricular cardiac atlas built from 1000+ high resolution mr images of healthy subjects and an analysis of shape and motion[END_REF], serves as a benchmark. The conjugate action of two transformations is defined as

Conj Φs (Φ t ) = Φ s Φ t Φ -1
s . Numerically, it can be computed as the solution of exp(trans(v t )) = exp(v s ) exp(v t ) exp(-v s ) in the SVF setting using iterated BCH formulas.

Experiments

Materials

We assess our methods on a 4D cardiac database of right-ventricular (RV) meshes. The population includes 34 healthy subjects, and 104 subjects with Table 1. Numerical consistency of parallel transports. Fiducial localisation error due to shape registration (left) and to forward/backward transport (right) (µ ± σ in mm).

Registration error (FLE) SVF 0.15 ± 0.15

Inverse Transport

Pole ladder SVF Conjugate SVF 0.12 ± 0.10 0.22 ± 0.12 pulmonary hypertension, which are divided into three classes according to the severity of the disease (New York Heart Association -NYHA, classes II, III and IV). The motion of the myocardium was given by point-to-point correspondences from commercial speckle-tracking of the RV from 3D trans-thoracic echocardiography (by 4D RV Function 2.0 software, TomTec Imaging Systems GmbH, Germany). For the acquisition of images, please refer to [START_REF] Moceri | Three-dimensional right-ventricular regional deformation and survival in pulmonary hypertension[END_REF].

Template Estimation and Registration

The meshes were spatially aligned at baseline time, end-diastole (ED), using rigid deformations with the iterative closest point algorithm. Then for meshes of different instants but belonging to one subject, we preserved their relative position between cardiac sequences by applying to them the same rigid deformation.

A template was built at baseline time ED as a mean shape in the healthy group using point distribution model. Then we compute the deformation from each subject's shape at ED towards the template. The middle point on this geodesic serves as the midpoint for the two symmetric mappings in pole ladder to transport temporal deformations, [M, S ], [M, T ] and [T, T ], [T, T ], as shown in Fig 2 . The computation of SVFs is implemented in C++.

Consistency

Inverse consistency was tested by transporting the velocity field corresponding to the end-diastole-end-systole (ED-ES) deformation forward along the geodesic encoding the subject-specific RV shape changes with respect to the template at ED, and then backward along the reverse geodesic. If the numerical implementation is accurate, the result of the inverse transport should be exactly the original vector.

Consistency was quantified by the error between the final warped end-systole (ES) shape and the original subject's ES shape (Table 1). The errors should be compared to the mismatch of each registration method (fiducial localisation error of vertices). We can see that SVF pole ladder transport was very consistent.

Application to the Statistical Modeling of Cardiac Deformation

In this subsection, we model ED-ES deformation in the whole subgroup of healthy subjects using parallel transports. Similar to the first step described in the previous experiments, we transported the velocity fields associated to each subject's ED-ES changes to the template at ED. Then, we applied principal component analysis (PCA) on the transported velocity fields, and warped the template with resulting principal components to show the main modes of deformation among this subgroup. We also compared this with the PCA modes obtained from the point-to-point ED-ES displacement. The first mode from point-topoint displacement accounts for the elongation (no relative displacement of the two valves), the second accounts for the vertical displacement and a slight orientation of the tricuspid valve. The first two modes from the pole ladder with SVF are mainly related to the orientation and the relative position of the tricuspid valve and the pulmonary valve. Figure 3 summarizes these results for the point-to-point displacement and pole ladder with SVF. We compared the compactness of the representations (Table 2) and found pole ladder with SVF a very good explanation.

Limitations

Cardiac motion tracking establishes point-to-point correspondences between mesh vertices, available here to benchmark our method. For databases that do not have such correspondence, one option is to register the segmented surfaces to the template, with the framework of currents or varifold-based deformation, which provide elegant mathematical approaches to match surfaces and establish point-to-point correspondence. The limitation of the method notably lays in registration accuracy, but this is compensated by the stability and one-step transport structure of the algorithm.

Conclusion

We proposed a general scheme to perform statistical modeling of the temporal deformation of the heart, directly based on meshes. The extensions of the pole ladder for parallel transport to mesh deformations were stable and accurate, of importance for the assessment of pathological changes. They also provided a more compact and interpretable representation that is useful for statistical modeling, and prevented surface folds in the range of population variability.

The method is adaptable to other anatomies with temporal or longitudinal data. Perspectives notably include synthetic experiments; the possibility to simulate physiologically-realistic motion on a given subject's anatomy, of relevance to better understand shape and motion interactions, or inversely to generate template sequences derived from populations, to be used for physiological modeling.

Fig. 1 .

 1 Fig. 1. Illustration of parallel transport of vectors a and b along a curve (left) and its application to cardiac imaging (right) with a focus on surfaces.

Algorithm 2

 2 Mid-point symmetric pole ladder transport of the geodesic segment [S, S ] along the geodesic [S, T ] -Compute the midpoint M = γ [S,T ] ( 1 2 ) on the intersubject geodesic; -Compute the symmetric point T = exp M (-log M (S )) of S with respect to M ; -Compute the symmetric point T = exp T (-log T (T )) of T with respect to T , and return the geodesic segment [T, T ].

Fig. 2 .

 2 Fig. 2. The symmetry-based pole ladder structure.

Fig. 3 .

 3 Fig. 3. Fist two modes of variation after applying PCA on the transported ED-ES changes, for the healthy subgroup. Comparison of point-to-point (top) and pole ladder with SVF (bottom). Surface folds appear at the arrow.

Table 2 .

 2 Compactness of the representations

	Explained variations 85% 95% 98%
	Displacement	6 11 16
	Pole ladder SVF	7 10 14

Acknowledgments. Part of the research was funded by the Agence Nationale de la Recherche (ANR)/ERA CoSysMed SysAFib project. The authors would like to thank fellows from Hôpital Pasteur, CHU de Nice, France for preparing the data.


V Sarou-Kanian

S Ouazar

P Escot Bocanegra

C Chauveau

I Gökalp

Low Temperature Reactivity of Aluminum Nanopowders with Liquid Water

In this paper, we present an experimental study of the isothermal reaction of aluminum nanoparticles with liquid water in the temperature range [45 -95°C]. Gas phase chromatography and X-ray diffraction analyses have revealed that the reaction Al + H 2 O yields to a solid aluminum oxyhydroxide (AlOOH) and to hydrogen (H 2 ). Hence, in order to describe the macrokinetics of the oxyhydroxidation of aluminum, the H 2 gas release was measured as a function of time and temperature. Furthermore, the effect of salt water (3% NaCl or KCl in mass) compared to pure water was investigated. It is shown that the hydrogen release is preceded by an induction period corresponding to the destruction of the oxide film initially covering the Al particles. The induction and the maximal hydrogen flow rate follow an Arrhenius law. Activation energies are calculated. In opposition to the works about the corrosion of salt water, the kinetics of reactions are slowed down by the addition of chloride ions.

Introduction

According to scientists hydrocarbon energies will soon be short supply. In the present context it is primordial to try to develop alternative energies as renewable energies for medium and long term applications. The hydrogen production may partially meet consummation need. The hydrogen is an abundant element on earth but it is found in hydrogenated compounds (water, hydrocarbons...). Today most of the hydrogen is produced from oil and others fossil fuels. This paper presents an alternative method for hydrogen production from aluminum nanoparticles reacting with water.

Experimental

Aluminum Nanopowder

Aluminum is known to be among the most stable metals in terms of resistance to oxidation. This physicochemical property has thus promoted its use, pure or alloyed, in numerous industrial applications (transportation, construction, packaging…). However, the corrosion of aluminum and its alloys by water has been widely investigated [START_REF]ASM Specialty Handbook, Aluminum and aluminum alloys[END_REF]. Even if the corrosion of aluminum by water is remarkably slow or absent in normal conditions, it can be favored by increasing temperatures, the pH, or the salinity of the aqueous solution. Furthermore, it has been shown that nanosized aluminum particles were particularly reactive with water [START_REF] Ivanov | [END_REF]3]. Ultrafine aluminum powders (UFP) are produced since some decades yet. There are several methods, but the exploding wire method is the most wide-spread. By this process a strong electric current is sent through an aluminum wire which explodes; the vaporization/condensation so yields to nanoscaled spherical Al powders. The Al particles obtained is called Alex (Aluminum Explosive, commercial name) and have a set of unusual properties in comparison with the usual metal [4,5]. It was found that oxidation of Alex particles occurs at a lower temperature with a higher rate of conversion. This is believed to be mainly due to the higher reactivity associated with greater surface area of the Alex particles. For this reason, Al nanopowders can be found covered with different sort of materials to prevent risks of self-ignition. Al nanoparticles used in our experiments are Russian commercial powders with a gaussian particles diameter distribution. The mean diameter is 100 nm and the full width at half maximum (FWHM) is 50 nm (Figure 1). This powder is passivated in air with a thin natural alumina coating (Al mass fraction=0.92, i.e. Al 2 O 3 thickness=1±0.5 nm).

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above 90°C the reaction was too intense to measure precisely the gas release.

During the investigations, distilled water was used in a wide excess in order to limit the effect of the heat released by the reaction. Isothermal processes are required to determine the influence of the temperature on the gas release. The following mixture was chosen: 60 g of distilled water and 0.1 g of Alex powder (0.17%weight of Al).

Our saline solutions have been obtained by dissolution of KCl(s) and NaCl(s) crystalline powders. The molar concentration is 0.95 %, i.e. near the sea salt concentration.

Figure 2 illustrates the experimental installation. The evolution of gas was measured with a graduated testtube (precision 1 ml) authorizing the measurement of volume according to time. The mixture temperature was also followed by a type K thermocouple connected to a thermograph. The procedure first consists to heat the 60 g of water in a closed system with a hot plate stirrer. The reactor is immersed in an oil bath. Two magnets allow the temperature homogeneity in the reactor and in the oil bath. When the temperature reached the required temperature, a mixture with 100 mg of Alex powder and 1 or 2 ml of water is prepared and then is introduced with a syringe in the reactor through a little orifice. According to Ivanov et al. [START_REF] Ivanov | [END_REF] the 100 mg of powder should product about 120 cm 3 of hydrogen. After each experiment the hydrogen gas volume is plotted as a function of time, and the maximal hydrogen flow rate is deduced by derivation of the curve. This parameter will characterize the kinetics of reaction.

Results and discussion

The reaction between water and Alex powder at low temperature The reaction between water and Alex powder in the temperature range [45-90 °C] involves the production of a gas and a white solid powder. The gas-phase chromatography revealed that the gas was dihydrogen (H 2 ). The solid phases characterized by X-ray diffraction are aluminum oxyhydroxide AlOOH also called boehmite with small amounts of unreacted aluminum (Figure 3). The broadening of the peaks of AlOOH shows that the crystallites size is very small and are around 5-10 nm. Furthermore, observations with TEM of the aluminum oxyhydroxide phase show that the product is in the form of "thin layers" (Figure 4). A significant number of experiments (85) have been performed and gathered in series corresponding to the study of the influence of the temperature on two kinds of solution: pure water and saline solution. Figure 5 illustrates the gas evolution process for different temperatures in pure water. First it is observed that the reaction occurs after a period called induction period (t ind ) during which no gas release is observed [START_REF] Ivanov | [END_REF]6]. Rat'ko et al. [6] suggest that this period corresponds to the hydration of the oxide film initially covering the aluminum particle surface. The oxide Al 2 O 3 is hydrated which leads to the formation of the complex Al 2 O 3 (H 2 O) x (where x is equal to 2 or 3). This compound is a porous oxide-metal composite material, so the hydration of the oxide film affects its homogeneity and continuously promoting the access of water to the metal surface and the occurrence of chemical reactions. The hydrated complex is then dissolved and finally precipitates in boehmite [8]. For each experiment the induction period was measured. Then the hydrogen degassing really starts with a "S shaped" gas evolution. It can be observed that the value of the volume theoretically released is not reached (1350 cm 3 H 2 /g Al). Many reasons can be considered. The oxyhydroxidation of the powder may be incomplete; the presence of Al traces is revealed by the X-ray diffraction diagram (Figure 3). Furthermore, small amounts of Al powder stick on the walls of the syringe during injection and are estimated as 3% of total weight. Here the conversion rate is defined by the ratio of gas volume released during the reaction to the volume that should has been released in theory for the same mass of aluminum. However above 75°C the conversion rate tends to the unity. The conversion rate increases like the increase of the temperature.

As the gas release is measured at a function of time, its temporal derivative represents the hydrogen flow rate. The maximal gas flow rate has been considered. Our results are compared to those of Ivanov et al. [START_REF] Ivanov | [END_REF] and Lur'e et. al. [7] who worked on nanoparticles of aluminum. However precise characteristics of their powders are not given in their papers.

Induction period

The induction period is measured experimentally as the period between the injection of the powder in the reactor and the appearance of the first gas bubble. Figure 6 illustrates the variation of t ind as a function of the temperature for pure and salt water. It is observed that the induction period follows an Arrhenius law for both of our solutions such as:

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ - ⋅ = ∞ RT Ea exp t t ind ind

Gas evolution

To characterize the reaction kinetics, the maximal hydrogen flow rate is considered. Figure 7 illustrates the variation of W max as a function of the temperature for both solutions. Results from Ivanov et al. [START_REF] Ivanov | [END_REF] and Lur'e et al. [7] also plotted even if our knowledge on their aluminum powder is very tight. According to Ivanov et al. [START_REF] Ivanov | [END_REF], the maximal flow rate is expected to follow an Arrhenius law, similar to the induction period: As for the induction period, the parameters of the Arrhenius law are summarized in Table II

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ - ⋅ = ∞ RT Ea exp W W max max THIRD EUROPEAN COMBUSTION MEETING ECM 2007

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Discussion

First it can be stated that the replacement of KCl instead of NaCl in saline solutions do not modify the reaction process. Indeed the kinetic parameters (t ind and W max ) belong to the same curves, so it appears that K + and Na + ions played similar roles. The remarkable point concerns the comparison between pure and salt water. It is clearly observed that the induction period and the maximal hydrogen flow rate in both solutions are different. t ind in salt water is longer than in pure water, and W max is lower in salt water than in pure water. Such results seem to suggest that saline solutions tend to slow down the reactivity of the oxyhydroxidation of Al nanoparticles. This observation is really surprising because it has been shown that salt water promotes the corrosion of pure or alloyed aluminum [START_REF]ASM Specialty Handbook, Aluminum and aluminum alloys[END_REF]. Indeed, aluminum corrosion is particularly sensitive to chloride solutions in the field of pitting corrosion [9,[START_REF] Reboul | Techniques de l'Ingénieur[END_REF]. In this kind of corrosion, chloride ions attack the defaults of the oxide film and allow to the water to access directly the aluminum surface. The contradiction of our results with the whole community of aluminum corrosion is questionable and no explanation can be reasonably given here. However, it has to be noticed that nanoparticles were used in this study, and it has been already observed that aluminum particles have unusual properties in comparison to micrometric particles or an aluminum bulk.

Concerning the influence of the temperature on the reactivity of aluminum nanopowders with pure and salt water, it is clearly shown that the induction period and the maximal hydrogen flow rate follow an Arrhenius law. It has also to be remarked that the Alex powder exhibits the most efficiency (lower t ind and higher W max ) compared to previous works [START_REF] Ivanov | [END_REF]3,7].

The activation energies for the induction period are the same for pure and salt water (80 kJ/mol). This value is close to the activation energy for the surface hydrolysis of amorphous oxide (71 kJ/mol). Vedder and Vermilyea [8] noticed that this value was also close to the activation energy of the proton diffusion in many oxides, and suggested that the proton diffusion may be an important step of the hydrolysis mechanism.

The activation energy for the maximal hydrogen flow rate is higher for pure water than for salt water (+20%). These results are in good agreement with [START_REF] Ivanov | [END_REF]3,7]. However, the maximal hydrogen flow rate does not describe completely the kinetics of oxyhydroxidation of aluminum. As Ivanov et al. [START_REF] Ivanov | [END_REF] suggest, the value of W max corresponds to the main stage of hydroxidation that is without the decelerating phase ('S-shaped'). In this case, the kinetic process is similar to a zero-order reaction.

Conclusion

The temperature dependence and the influence of the salinity have been investigated for the reactivity of aluminum nanoparticles with water. It has been shown that the production of hydrogen is preceded by an induction period corresponding to the hydrationdissolution-precipitation of the oxide film initially covering the particles. This induction period is thermally activated (Ea=80 kJ/mol). The hydrogen released by the reaction (oxyhydroxidation) and characterized by W max is also thermally activated with similar values of Ea found in the literature. Contrary to the literature on the corrosion of aluminum in salt water, the oxyhydroxidation of the nanopowder is slowed down in the presence of chloride ions.

Further work will be led to complete the investigation. Saline solutions with different concentrations will be tested to study the influence of the salinity on the kinetic parameters (t ind , W max ). Al nanopowders with different particle sizing and/or coating will be also examined. Indeed, as the specific surface increases with the reduction of the diameter of particles, one expects to observe higher maximal flow rates for smaller aluminium particles. In conclusion, the influence of the pH also could be studied.

Fig. 1 :

 1 Fig. 1: Image of the Alex powder by scanning electron microscopy. Experimental set-up The aim of our experiments is to study the reaction Al + H 2 O with variations of two parameters: the temperature and the salinity of the solution.The experiments were carried out in the temperature range [45 -90°C]. Indeed, for temperatures higher than 45°C the reaction occurs significantly. On the contrary,

Fig. 2 :

 2 Fig. 2: Experimental set-up. (1) Graduated test-tube. (2) Type K thermocouple. (3) Reactor with 60 g of water. (4) Hot plate stirrer. (5) Oil bath. (6) Syringe with the mixture Al+H 2 O. (7) Vacuum pump.

Fig. 3 :

 3 Fig. 3: Diffraction diagram of the Al+H 2 O reaction residues. •: AlOOH (JCPDS 00-049-0133); □: Al (JCPDS 01-085-1327)

Fig. 4 :

 4 Fig. 4: Image of the solid product by transmission electron microscopy. These analyses suggest that the aluminum powder conversion process in water for the temperature range [45-90 °C] is such as: Al(s) + 2 H 2 O(l) AlO(OH)(s) +3/2 H 2 (g) In theory a mass of one gram of aluminum should lead to a release of 1350 cm 3 of H 2 at 20°C. A stoichiometric mixture has a composition of 57 % of water and 43 % of aluminum in mass proportion.

Fig. 5 :

 5 Fig. 5: Gas evolution process in water for different temperatures.

Fig. 6 :

 6 Fig. 6: Induction period as a function of the temperature for pure and salt water.

Fig. 7 :

 7 Fig. 7: Maximal hydrogen flow rate as a function of the temperature and for pure and salt water.

Table I :

 I

		t	∞ ind
	Solution		∞ ind t (s)	Ea (kJ/mol)
	H 2 O	6.41 10 -11	-79.9 ± 4.1
	NaCl, KCl solutions 1.12 10 -10	-80.4 ± 4.3

Table I :

 I Arrhenius law parameters for the induction period.

Table II :

 II . Arrhenius law parameters for the maximal hydrogen flow rate.

	Solution	∞ max W	Ea (kJ/mol)
		(cm 3 /g/min)
	H 2 O, present work	1.90 10 14	77 ± 1.5
	H 2 O, Ivanov et al. [2]	7.93 10 15	89 ±1.5
	H 2 O, Lur'e et al. [7]*	3.02 10 14	85 ± 4.3
	NaCl, KCl solutions, present work	7.70 10 11	62 ± 3.5

* for micrometric powders

(3-4 µm)