François Galasso
email: francois.galasso@mines-albi.fr

Yves Ducq
email: yves.ducq@u-bordeaux1.fr

Matthieu Lauras
email: matthieu.lauras@mines-albi.fr

Didier Gourc
email: didier.gourc@mines-albi.fr

Mamadou Camara
email: mamadou.camara@u-bordeaux1.fr

A Method to Select a Successful Interoperability Solution through a Simulation Approach

Keywords: Collaborative Network, Interoperability, Performance Measurement System, Decision Support System, Simulation

Enterprise applications and software systems need to be interoperable in order to achieve seamless business across organizational boundaries and thus realize virtual networked organizations. Our proposition can be considered as an interoperability project selection approach and is based on 3 steps: (1) Modelling both collaborative business processes and potential related interoperability projects; (2) Evaluating the accessibility of each project regarding the current state of the organization; (3) Simulating each project and assessing the associated performance. These results are finally projected on a comparison matrix used as a decision support to select the most appropriate interoperability solution. An application case extracted from the French aerospace sector demonstrates the applicability, the benefits and limits of the proposition.

Introduction

There is a growing interest in solutions enabling companies to work together more effectively. A wide variety of collaborative systems exists and addresses different aspects of this complex problem while providing different benefits to networked enterprises. Thus, enterprise interoperability is crucial for companies and especially in decentralized, flexible and networked manufacturing system environment.

Interoperability is defined as "the ability for a system or a product/service to work with other systems or products/services without special effort of the part of the user" [START_REF] Chen | Architectures for enterprise integration and interoperability:Past, present and future[END_REF]. Enterprise Interoperability (EI) is defined as "the ability of an Enterprise to interact with other Enterprises not only on an Information Technology point of view but also on organisational and semantic point of views. This interaction must be flexible and developed at the lower cost" [START_REF] Interop | Enterprise Interoperability-Framework and knowledge corpus -Advanced report[END_REF].

Enterprise applications and software systems need to be interoperable in order to achieve seamless business across organizational boundaries and thus realize virtual networked organizations. But interoperability should not only be considered a property of informatics systems. The diversity, heterogeneity, and autonomy of software components, application solutions, business processes, and the business context of an enterprise must also be considered [START_REF] Chen | Interoperability Knowledge Corpus, Deliverable DI.1b, Workpackage DI, INTEROP NoE[END_REF].

But in practice, networked business encounters recurrent difficulties and only very limited success has been made due to the ongoing evolution of systems, the speed of market changes and growing complexity (Panetto and Molina 2008), [START_REF] Jochem | Enterprise Interoperability Assessment[END_REF]. Facing this huge complexity, decision-makers are confronted to the difficulty of choosing an accurate and relevant interoperability investment for their networked enterprises.

An interoperability investment is intended to improve interactions between enterprises of the network in general (or supply chain) by means of technological solutions. The interoperability project is the planning and implementation of the interoperability investment. Qualitative and quantitative approaches were developed previously in the literature to measure and improve interoperability. Those approaches do not propose any mechanisms for prior validation of interoperability solutions. By prior validation we mean being able to evaluate, earlier in the project, the two following elements: the potential improvement that will result from the solution's implementation; and the impact of this interoperability improvement on the achievement of objectives of enterprises in the network at operational, tactical and strategic levels.

As for any decision-making, such a choice depends on the capacity of the decision maker to assess: (i) the current situation -What happened until today? What is the current progression (in a broader sense)? -and (ii) the possible interoperability solutions and their related impact (information systems, business processes, organizational…) -What will happen and what are the consequences for the network?

Performance evaluation appears as a natural tool to design/modify/improve the interoperable solution of a networked enterprise. But judging an interoperability solution's performance in practice is very situation-specific and so complicated.

In accordance with the above, the objective of this paper is to present a complete methodology in order to help decision-makers for the selection of the best interoperability solution (or at least the most appropriate), proposed in a project for their businesses at the scale of the network. Concretely, the method must enable to a priori evaluate and compare the performance of different interoperability solutions in a networked enterprise. This research work is a part of the French ISTA-3 research project (3rd generation Interoperability for Aeronautics Sub-contractors).

The paper is divided into three main parts. Firstly, the literature related both to performance measurement systems in general and to performance for interoperability are discussed as well as literature dedicated to project management. From this background, our research statement is justified and exposed. Then the proposed method is presented in order to: (i) evaluate and compare interoperability solutions in a networked enterprise by exposing how to evaluate the accessibility of a project; (ii) evaluate the whole performance of each solution in order to select the most appropriate one. Next, a real case application relating to an aerospace network is presented. Conclusions and perspectives of this methodology are given at the end.

Literature Review

From Performance Measurement to Interoperability Measurement

When defining a method to select an interoperability solution based on its performance improvement, the first literature review must be dedicated to performance measurement methods from the general ones to those dedicated to interoperability measurement.

The domain of performance measurement has been investigated for more than twenty years leading to a lot of methods around the world, developed either by researchers or practitioners, in order to define and implement indicators. All these methods have been developed independently based on system theory, production management theory or accounting methods, according to the background of developers. [START_REF] Ravelomanantsoa | Contribution à la définition d'un cadre générique pour la définition, l'implantation et l'exploitation de la performance : Application à la méthode ECOGRAI[END_REF] has identified more than thirty methods for Performance Measurement System (PMS) definition and implementations, covering methods, tools, models, and generic list of Performance Indicators (PI). Among all these thirty methods, more or less used and well known, one can cite the famous ones or the most used or disseminated around the world as Balanced Score Card (BSC) [START_REF] Kaplan | The Balanced Scorecard[END_REF][START_REF] Neely | The performance prism:The scorecard for measuring and managing business success[END_REF][START_REF] Ducq | Definition and aggregation of a Performance Measurement System in three Aeronautical workshops using the ECOGRAI Method[END_REF][START_REF] Bititci | Integrated Performance Measurement System: a development guide[END_REF][START_REF] Ghalayini | An integrated dynamic performance measurement system for improving manufacturing competitiveness[END_REF].

However, all these methods being mainly developed for generic PIs, none of them are dedicated to the measurement of interoperability performance. For instance, in the BSC, no perspective is dedicated to collaborative performance, as well as in PRISM or in QMPMS. Indeed, all these methods are dedicated to measurement of performance of a single company and interoperability aspects are not addressed.

For instance, even if BSC has been applied to many different companies, no example are proposed for interoperability because it is quite impossible to relate the perspectives (financial, customer, organisation & learning and internal processes) with the notion of interoperability. So PI related to internal processes could do the job but this is very limitative in comparison to the balanced and transversal principles of the method. Another solution could be to weight the BSC Perspectives according to interoperability challenges but this would be difficult to implement and would depend too much on the expert point of view.

Other models have been developed as Supply Chain Operational Reference model (SCOR 2010) or Value Reference Model, which provide pre-defined measurable PI for Value Chain goals in several dimensions (Value Chain Group 2012). However, no PI dedicated to interoperability as well as PI dedicated to the measurement of interoperability impacts are proposed.

Existing metrics dedicated to interoperability measurement have been analyzed in [START_REF] Chen | Barrier driven methodology for enterprise interoperability, PROVE2007[END_REF] who considered three types of interoperability measurement: (i) potential measurement (interoperability level whatever the partner is), (ii) compatibility measurement (interoperability level according to a specific partner to remove barriers) and (iii) performance measurement during the operational phase using performance metrics of time, quality and cost of interoperation between two companies.

However, as for the previous models the concepts are defined but no PI is proposed to measure interoperability. Nevertheless, the performance metrics of time, quality and cost of interoperation between two companies, will be considered in our proposed method.

Even if some metrics dedicated to interoperability measurement have been proposed, they are not related to traditional business performance metrics in order to show the impact of interoperability improvement on the business performance in particular at the network level. The challenge is to propose strategic PI based on detailed measures (business and interoperability measures) in order to detect the best interoperability solutions at the level of the network. About this challenge, several authors pointed out the need for the community and practitioners to develop accurate and relevant performance measurement approaches able to support decision-making in interoperable environment. However, for many years, specialists [START_REF] Beamon | Measuring Supply Chain Performance[END_REF][START_REF] Gunasekaran | Performance measures and metrics in logistics and supply chain management: a review of recent literature (1995 -2004) for research and applications[END_REF][START_REF] Akyuz | Supply chain performance measurement: a literature review[END_REF] have highlighted the limitations at the networked scale of solutions described previously and in use today.

Recently, authors such as [START_REF] Gunasekaran | Performance measures and metrics in logistics and supply chain management: a review of recent literature (1995 -2004) for research and applications[END_REF]; [START_REF] Alfaro | Business process interoperability and collaborative performance measurement[END_REF]; [START_REF] Akyuz | Supply chain performance measurement: a literature review[END_REF] have confirmed that academics and practitioners are still in need of a new PMS, which can handle the requirements of the new enterprise networks. These authors affirm that such a PMS dedicated to interoperability should measure, locally and globally, the performance of the network in order to make decision at the global level to the best interoperability solution. They explain that there is a need for a PMS to assess in advance the potential results of one or another interoperability solution. This is the finality of a priori performance evaluation.

A priori performance evaluation consists in anticipating the future performance of the system (in our case, of the networked enterprise). This includes three main steps: (i) Innovation: explanation and objectives; (ii) Implementation: variables and indicators choosing; (iii) Observation: simulation through a model. This kind of performance evaluation is based on an enterprise model and on a simulation approach to evaluate the probable future results of each PI (local and global in our case). One main difficulty relates to the design of the model and the link to the simulation approach.

Consequently, a PMS dedicated to interoperability should be based on accurate and relevant enterprise models (that is to say, a business process model able to focus on interoperability components of the network) on one hand, and based on a associated simulation tool (that is to say, a tool able to simulate the previous enterprise modelling and to measure the different KPI) on the other hand.

Interoperability Projects

Interoperability solutions can only be considered through the projects that implement them. Project can be defined as "a temporary undertaken to create a unique product, service or result" [START_REF] Pmi | A guide to the project management body of knowledge[END_REF]. Professional organisations as well as standards bodies have for several years produced guides and books on project management and good practice. For instance, PMI (Project Management Institute) developed a guide to the Project Management Body of Knowledge (PMBoK) [START_REF] Pmi | A guide to the project management body of knowledge[END_REF]. This guide is process-based, meaning it describes the work as being accomplished by processes, structured as nine knowledge areas. It offers project manager's processes they have to implement and the indicators they have to manage in order to reach project objectives. Among these knowledge areas we can cite as example: Project Scope Management; Project Time Management; Project Cost Management; Project Quality Management; Project Human Resource Management and Project Risk Management. Our method is consistent with PMBoK as other management standards like Software Engineering Institute's CMMI and Prince2.

Interoperability project can be characterized as a collaborative project with an interest to develop an interoperability solution within a networked organization. Despite numerous improvement efforts, many interoperability projects have problems to be delivered on time, within budget, with all the required features and functions. Actually, notably due to the distributed nature of the stakeholders, the project management success, the project success and the product success of this kind of project are not guaranteed. Considering that the project size influences budget and project quality, while project complexity influences the use of specific project management practices [START_REF] Martin | IS Project Management: Size, Complexity, Practices and the Project Management Office, System Sciences, HICCS'05[END_REF], we could explain this fact by the:

-Inherent complexity of such a project; -Difficulty to predict cost-benefit ratio.

The definition of project complexity has been covered by various contributions and research works (see [START_REF] Baccarini | The concept of project complexity -a review[END_REF] and [START_REF] Vidal | Measuring project complexity using the Analytic Hierarchy Process[END_REF] for a survey on this subject). In summary, project complexity can appear in different forms and arise from various sources with different levels of intensity. Intensities can vary over time, and this variation underlines the dynamic aspect of project complexity. [START_REF] Baccarini | The concept of project complexity -a review[END_REF] explains in his review of literature that complexity is a distinctly different concept to two other project characteristics: size and uncertainty. Both practitioners and academics have difficulties accepting and treating projects as complex systems, and tend to reduce the management of projects to the application of tools such as PERT, WBS, earned value, etc. [START_REF] Geraldi | On faith, fact, and interaction in projects[END_REF]. When complexity becomes too great, the possibilities and interrelations become so fuzzy that the system has to be assisted by appropriate tools and skills. Consequently, managers facing complex projects, such as interoperability projects, need access to a decision-making aid model.

This point clearly justified the purpose of this paper that consists in supporting the choice of the best interoperability solution and by the way the best interoperability project, in a given environment.

Over the years a variety of techniques have been proposed to help solving the problem of making accurate, yet early, project predictions in order to make good project selection. The existing methodologies for project selection range from multiple criteria scoring models and ranking methods to subjective committee evaluation methods [START_REF] Blanc | Contribution à la caractérisation et l'évaluation de l'interopérabilité pour les entreprises collaboratives[END_REF]. In both categories, the project prediction is organized following two dimensions that are: (i) the potential result of the project (kind of "benefit") and (ii) the potential effort to produce to operate the project (kind of "cost").

This potential effort considers the gap between the current and expected state of the enterprise and characterises what will be called the "accessibility" of a project hereinafter.

In the previous section we presented a background on existing methods able to assess the performance of an interoperability solution. In other words, we discussed about the performance of the deliverable of an interoperability project. In this section, we are studying the second dimension of the problem by discussing how decisionmakers can dread the difficulty to operate such or such project corresponding to such or such interoperability solution.

Numerous models and methodologies have been developed to support project managers in dimensioning their projects. Many of them involve the use of historical data (from previous projects) in order to develop prediction systems. Different factors are considered to size the project effort: number of people working on the project, length of the project, budget allocated for the project, etc. Some approaches allow doing that by involving the use of general models or prediction systems that are parameterized to account for differences between project environments. The most known examples in Information Systems domain are COCOMO (Constructive Cost Model), COCOMO 2.0, and Function Point analysis [START_REF] Boehm | Cost models for future software life cycle processes: COCOMO 2.0[END_REF]. These approaches need to estimate input parameters like thousands of source lines of code (SLOC) in a numerical unit (COCOMO approach). The capacity of estimating this input parameter depends on the availability of formal historical data on past projects or the availability of human competencies in the organization for an assessment by analogy.

Classically, companies have no or very few experience in terms of interoperability project. In fact, the concept is relatively new and generally the selection and the implementation of an interoperability solution is a one-shot operation for a company.

Consequently the use of mathematical effort estimation methods, like COCOMO or Function point method, seems to be difficult in such a context and probably the use of more qualitative approach should be used to assess the accessibility of an interoperability project.

Nevertheless, this accessibility depends on a lot of quantitative and qualitative criteria. Researchers proposed review of criteria depending on domain of projects [START_REF] Badri | A comprehensive 0-1 goal programming model for project selection[END_REF][START_REF] Lee | An integrated approach for interdependent information system project selection[END_REF][START_REF] Wen | Measuring e-commerce efficiency: A data envelopment analysis (DEA) approach[END_REF][START_REF] Sowlati | Information systems project prioritization using data envelopment analysis[END_REF][START_REF] Mahmudi | Selecting the most efficient information system project using data envelopment analysis: Case Study of Iran Ministry of Commerce[END_REF].

So, based on this literature review and in the context of interoperability projects, we propose an approach of effort estimation based on technical/complexity criteria which are valuated with symbolic modalities. If numerical data are available for statistical analysis, the proposed approach could be adapted to integrate these results.

The next section presents the proposed methodology to measure interoperability and to select the best appropriate project to solve interoperability problems.

Interoperability Project Selection Methodology

Overview and Assumptions

Our proposition is based on two main assumptions. First, all partners of the network are considered to have already implemented a PMS and consequently get their own PI able to measure their local performance. Second, decision-makers are able to define and model several options to support their interoperability needs. For instance, they could envisage and describe a solution associated to each existing level of interoperability [START_REF] Clark | Organisational Interoperability Maturity Model for C2[END_REF]:

-Independent: these are organizations that would normally work without any interaction other than that provided by personal contact; -Collaborative: these are organizations where recognized frameworks are in place to support interoperability and shared goals are recognized and roles and responsibilities are allocated as part of ongoing responsibilities however the organizations are still distinct; -Combined or Integrated: these are organizations where there are shared value systems and shared goals, a common understanding and a preparedness to interoperate; -Unified: these are organizations in which the organizational goals, value systems, command structure/style, and knowledge bases are shared across the system.

Our proposition can be considered as an interoperability project selection step. Classically, the process of project selection uses project evaluation and selection techniques in a progression of three phases: strategic considerations, individual project evaluation, and project selection [START_REF] Archer | An integrated framework for project portfolio selection[END_REF]. Thus, a three-step methodology is proposed to support decision-making in terms of selection of the best interoperability option (i.e. project) for a given network:

1. Modelling the collaborative processes and the different interoperability options (this is the Innovation part); 2. Evaluating the accessibility of each option (this is the Implementation part); 3. Simulating each option against several scenarios and assessing the expected performance (this is the Observation part).

The final objective of this approach is to build a decision-making support matrix (see. Figure 1) able to show, for each scenario, the balance between:

-The accessibility of the option: this deals with all concerns in a project evaluation step. Is the project accessible for the networked organization? Is it compatible with financial capacities and available means in the organizations? Does the organization have the skills to lead the project for implementing such an interoperability option? -And the expected performance for the partners: What will be the global network performance? So, the proposed approach is presented in the figure 2 below:

Expected Performance Fig. 2. Main steps of our proposed approach

Step 1: Modelling the Interoperability Options

The modelling of the interoperability options aims to represent the collaborative activities and interoperability nodes in the network. It allows understanding the complexity of the collaboration.

Even though different Business Process Modelling techniques could be envisaged, this is not the purpose of the present study to discuss such a choice. We have chosen to work with the Business Process Modelling Notation (BPMN) standard [START_REF] White | BPMN modeling and reference guide: understanding and using BPMN[END_REF]. This standard pays particular attention to both the sequencing of operations and the flows. It also gives the opportunity to study the interfaces, which facilitates the discussion of coordination and synchronization problems through a message flow between several separated processes stakeholders (business entities or business roles) who send and receive message [START_REF] White | BPMN modeling and reference guide: understanding and using BPMN[END_REF]. This point is particularly crucial within an interoperability project. However, any other modelling language based on the description of activities and sequence flows may be investigated and used. Moreover, BPMN is quite well defined by a strong meta-model proposed by OMG and so different kinds of software tools are proposed for free to support BPMN modelling.

Finally, another major interest of BPMN language for our research work is the fact that is relatively easy to simulate by classical tools of Discrete Event Simulation (native in the majority of simulation software) (see. Section 3.3).

Step 2: Evaluating the Accessibility of each Option

The goal of this step is to find out a measure at the project level for approximating in early stages the accessibility for the networked organization. The accessibility of a solution (an interoperability option) can be defined as a ratio between the needed efforts to develop this solution and the available means of the networked organization. In other words, it explains the capacity of the networked organization to conduce with success this change. In practice the accessibility dimension aims to assess efforts that each interoperability option (modelled in step 1) requires to be implemented in order to represent the different solutions on a common axis (from the least accessible solution to the most accessible one). In other words, for a specific networked organization, the more the project concerning the interoperability option is matched with the means of the organization, the more it is accessible (and vice-versa).

Based on the results of literature review in section 2.2, the following criteria are proposed to assess the accessibility of each scenario:

-Human resource requirement: Estimation of the effort to commit and the availability of the required skills; -Budget requirement: Estimation of the total cost of the project (investment, human resources, etc.) compared with the means of the organization; -Risk: Estimation of the negative risks the project has to cope with; -Cultural gap: Estimation of the cultural change scale.

Because an interoperability project is very dependent of the IT solution that will be deployed, our methodology is definitively built on the research work of [START_REF] Shenhar | Project success: A multidimensional strategic concept[END_REF]. In this research work, the authors distinguish the difficulty to operate such or such project by proposing to use the level of technological uncertainty at the moment of project initiation. This classification, which has been shown to be one of the major independent variables among projects, includes the following four levels and fit very well with the subject of interoperability projects:

-Low-Tech Projects rely on existing and well-established technologies. This level corresponds to a high level of accessibility, which is easy to implement for the organization;

-Medium-Tech Projects are mainly based on existing common technologies but (i) incorporate some new technology or feature or (ii) some of the planned technologies are not well controlled by the organization. This level corresponds to a moderate level of accessibility (reasonable to implement); -High-Tech Projects are defined as projects in which most of the technologies employed are new for the organization, but knowledge exists in other companies. This level corresponds to a low level of accessibility (difficult to implement); -Super High-Tech Projects are based primarily on new, not yet existent technologies, which must be developed during project execution. This level corresponds to a very low level of accessibility (very difficult to implement).

Our objective consists in assessing the studied interoperability projects by categorizing each option in one of the four previous levels. To reach this goal a quotation scale is defined that corresponds to the different levels of project. So, four levels of project accessibility are proposed: the Low level corresponds to the Low-Tech Project level; the Moderate level corresponds to the Medium-Tech Project level; the High level corresponds to the High-Tech Project level; the Extreme level corresponds to the Super High-Tech Project level. This quotation is applied to each of the four criteria presented previously: Human Resources Requirements, Budget Requirements, Risk, and Cultural Gap. Considering the classical project risk management recommendations, one makes the assumption that the quotation of the whole project corresponds to the highest quotation of each criteria. For instance, if the quotation for a project is {Human resources requirements = Low; Budget Requirements = Moderate; Risk = Low; Cultural Gap = Low} then the global project assessment will be Medium-Tech Project (Average Accessibility).

The following table summarizes this assumption.

Project Interoperability Level

Associated Accessibility Level

Human Resource Requirements

Budget Requirements

Risk

Cultural Gap

Low-Tech Project

High accessibility

Low

Low Low Low

Medium-Tech Project

Moderate Accessibility

Moderate

Moderate Moderate Moderate

High-Tech Project

Low Accessibility

High

High High High Super High-Tech Project

Very Low Accessibility

Extreme

Extreme Extreme Extreme

Tab. 1. Assessment of scenario Accessibility.

3.3.

Step 3: Evaluating the Performance of each Option

Step 3.1: Assessing All Performances for an Option

The third step consists in assessing the intrinsic performance of each option. As discussed in section 2.1, this performance might be evaluated using a simulation approach. In our case, we propose to simulate the BPMN diagrams produced in step 1 by using classical Discrete Event Simulation technique and software such as Witness ® or Arena ® . This principle seems to be relatively typical if we refer to the works developed by [START_REF] Enstone | BPMN and Simulation[END_REF] and traditionally composed of two main components: (i) simulation modelling and (ii) events list.

Regarding to the first component, a set of simulation models that corresponds to the different options described in step 1 is proposed. Concretely, for each BPMN model established in step 1, a simulation model is defined. These simulation models must include the intrinsic parameters that describe the own characteristics of each option as for instance:

-activities' runtime execution, -activities' non-quality rate, -activities' cost, -transmission lead times All these simulation models must be able to measure a priori the PI defined by decision-makers as representative of the interoperability impact of their collaborative processes. Then, for each PI, the operational performance of each interoperability solution (option) has to be monitored. It is important to underline that the PI must be common to all options and consequently to all simulation models for comparison purpose. These PI should be representative of the main interoperability stakes of the concerned project.

The second component of our approach consists in defining the common scenarios that has to be confronted to all interoperability solutions (options) in order to compare their relative performance. In fact, in discrete-event simulation, the operation of a system is represented as a chronological sequence of events. Each event occurs at a certain time and may induce a change of state in the system. These global schemes are thus called scenarios and include consequently a list of events that is the common inputs of all the simulation models. Some examples of events could be: customer orders (quantity, delivery time, etc.), demand or supply hazards, etc. These scenarios are simulated and the behaviour of each interoperability option against different situations is assessed.

To summarize, the third step of the proposed approach consists in:

1. Translating the BPMN models into a Discrete Event Simulation Models; 2. Defining a set of PI that are identical for all the options in order to be able to compare them; 3. Defining a set of scenarios (events) that is representative of the common outlines we want to simulate to compare the options;

4. Running the simulations on Discrete Event Simulation software: 1 simulation = {1 option; 1 scenario}.

Step 3.2: Evaluation of the Global Score for a Scenario

At this stage, the simulation brings a raw series of values regarding to each set {scenario, PI, option}. In order to be able to compare the performance of each interoperability option (and thus, to select the best interoperability solution for the network), an aggregation of the PI measures obtained for a given simulation (i.e. {1 experiment; 1 scenario}) is needed. By definition, the set of PI allows to measure the achievement of all aspects of an interoperability project. Nevertheless the aim is to produce a single reduced evaluation of the performance of each simulation, to support interoperability solution selection decision-making. This objective refers to [START_REF] Hansen | Exploratory performance assessment[END_REF] who oppose two fundamentally different approaches: the aggregate approach and the composite (partial) approach.

The principle of performance aggregation is to highlight the global performance based on detailed performance described using eventually several performance criteria. Most of the multi-criteria aggregation methods are using weighted average method as AHP, ELECTRE (ELimination Et Choix Traduisant la REalité), PROMETHEE (Preference Ranking Organisation Method for Enrichment Evaluations), MAUT (Multi-Attribute Utility Theory), but these methods are not very adapted to interoperability performance measurement because the weight is very subjective to the decision maker feeling which requires a lot of return on experience. In the domain of interoperability, this return on experience is not easy to obtain in particular when the collaboration is recent. Other researchers are developing new methods as Choquet Integral used in MACBETH (Measuring Attractiveness by a Categorical Based Evaluation TecHnique) method, which is based on the qualitative preferences of the decision maker that is considered as more intuitive than the quantitative preference. However this method is not yet established and its robustness is not guaranteed.

The composite approach consists in reducing the performance assessment to one or a limited number of PI that can be considered as representative of the whole performance of the system. From decision-makers point of view, this approach has the great advantage to produce measures easily interpretable. A method developed specifically for the performance composition approach is CPMM (Causal Performance Measurement Model). CPMM is used to outline the specific path that a company will follow to achieve its strategy [START_REF] Niven | Enterprise integration and interoperability in manufacturing systems: Trends and issues[END_REF]. To be deployed appropriately, a CPMM could be represented using either quantitative or qualitative techniques. A company can numerically estimate the strength of the relationships in its CPMM through a statistical analysis [START_REF] Epstein | Linking actions to profits in strategic decision making[END_REF][START_REF] Kaplan | The strategy-focused organization[END_REF]. Qualitative reasoning consists in developing programs that enable operations under a condition of insufficient numerical data or in the absence of such data [START_REF] Hamschera | Qualitative reasoning in business, finance, and economics: Introduction[END_REF]. This last situation corresponds exactly to our case. To create the CPMM, the cause-and-effect relationships in each pair of variables should be determinate: positive proportionality (P+), a negative proportionality (P-) or no relationship between the variables. Instantiating the qualitative model generates a qualitative prediction, in the form of intervals, for each endogenous variable, without specifying a precise numerical value [START_REF] Hinkkanen | A Set-Theoretic Foundation of Qualitative Reasoning and its Application to the Modeling of Economics and Business Management Problems[END_REF]. The qualitative value of a variable at a given state is described as its qualitative magnitude and the sign of its derivative. The sign of the derivative of a variable specifies the direction of change, which can be increasing, steady or decreasing.

Finally, the CPMM model allows aggregating the most representative PI in a single PI on which the comparison study could be based on. Then the value of this PI for each simulation {1 Option; 1 Scenario} will constitute the global score to compare between the scenarios.

Choosing the best Interoperability Option

This last step synthesizes all the previous results in a matrix aiming at supporting the decision-making (see. Figure 1). The Y-axis represents the aggregated value of the interoperability option performance (through the representative PI identified with the CPMM model) while the X-axis represents the value of the interoperability project accessibility (from the less accessible to the most accessible). Then a scatter plots will appear for a given option because:

-There is one accessibility score for one option; -There are several scores in terms of interoperability performance for a given option related to the different scenarios.

Finally, the decision-making is supported in analyzing the position of the scatter plots. Those that will be in a lower left corner would probably be the worst whereas those that will be in upper right corner would probably the best.

Application Case

The case study involves an enterprise producing moulds and is extracted from the French ISTA-3 research project. It considers a subcontractor (SUB1) in the aeronautical industry receiving files containing Computer Assisted Design (CAD) models for moulds from a main customer (MPN). Then SUB1 works with a second subcontractor (SUB2) in charge of designing tools and moulds for SUB1. The study is leaded considering SUB1 point of view. The PMS represents all of the indicators used to evaluate the impact of solutions. This PMS contains indicators grouped into three components: the operational, tactical and strategic PIs:

-Strategic level (dependent variables)

• Profitability per contract -Tactical level (intermediate variables)

• Cost of mould production • Number of defaults by produced item because of the tool (i.e. the tool used for supporting the interoperability dedicated activities) • Global lead time with defaults These PI assess solely the performance of the interoperability dedicated activities. The supply chain part of the activities (such as planning, manufacturing and even design...) is not taken into account.

In the scenario retained in our case study to realize the simulation, the following assumptions were made by the team:

-The variables Number processed files (number of iterations) and Number of moulds (number of iterations) are supposed to have a positive proportionality.

-The variables Number of defaults by file, Number of defaults by product because of the tool and Global lead-time with defaults have a negative proportionality. These proportionalities for the independent variables represent hypotheses about the direct impact of the proposed solution. The validation or rejection of the solution will be based on the conformity between prior estimated variations and the expectations. In our application, a decrease is predicted by the model for tactical measures Cost of mould production and Cost of file processing as expected through using a more performing interoperability solution. At the strategic level also, the increase of the variable Profitability per contract is expected. The proposed solution could be validated based on these results.

Discrete event simulation results

The discrete event simulation is based on a Witness® model close to the BPMN model firstly developed in order to assess the collaboration (as the result of the first phase of our methodology) between MPN, SUB1 and SUB2 and depicted by Figure 3. The PIs are obviously the same as defined in section 4.1.

The studied process concerning these three companies is composed of three main steps depicted in Figure 3: -Step 1: Feasibility: a file is received by SUB1 and then a first loop is engaged with SUB2 in order to evaluate the feasibility of the mould; -Step 2: Estimation/Ordering: if feasible, an estimate is sent to SUB1 by SUB2 and if SUB1 agrees it leads to an order for realizing the mould sent by SUB1 to SUB2; -Step 3: Validation: starts the concrete building of the mould by SUB2. Then, the mould is received by SUB1 and tested with few prototypes parts. In the meanwhile an invoice is sent by SUB 2 to SUB1. At each step, disruptions can exists leading to a comeback to the step n-1 or to a complete give-up of initial order from MPN. 1. Simple files: concern small or simple moulds. These simple files are easily handled by both SUB1 and SUB2, 2. Standard files: concern more complex moulds and represents the most important part of the files received by SUB1, 3. Complex files: concern complex moulds leading to the highest level of disruptions in the process and the highest give-up of the initial order. The simulations are developed according to three interoperability options graded from Low to High in terms of accessibility (see section 3.2):

-Option 1 is the most accessible scenario (graded High) in which the improvement of SUB1 interoperability dedicated activities is done through the use of an estimate management system; -Option 2 (graded Medium) is an extension of option 1 to the improvement of SUB2 interoperability dedicated activities in the management of the feasibility study (SUB2 gains access to the estimate management system of SUB1). -Option 3 (graded Low) is an improvement of information transfer through the use of a collaborative platform such as Mediation Information System: this simulates an improvement of interactions for each company.

Each option is evaluated regarding three scenarios distinguished by the percentage of each king of orders SUB1 and SUB2 have to deal with:

-Scenario 1: simple orders represent 35% of the projects, standard orders: 55% and complex orders: 10%, -Scenario 2: simple orders represent 10% of the projects, standard orders: 35% and complex orders: 55%, -Scenario 3: simple orders represent 55% of the projects, standard orders: 35% and complex orders: 10%.

Step 1

Step 2

Step 3

These three scenarios are simulated in order to assess the robustness of the interoperability scenario against a change in the activity of the company. This leads to 9 simulations.

The results of the simulation are given in It can be outlined, from Table 3, that the qualitative simulation corresponds to the results given by the discrete event simulation. As the level of interoperability increase for scenario 1 to 3, the IPs behave as predicted by the qualitative model. It can be noticed that in the case of scenario 3, moving from option 2 to 3 does not involve an important improvement of the IPs. Indeed, the scenario 3 is based on the less complicated orders. It can be guessed from these simulations that managing these simple orders does not require a high level of interoperability.

Figure 4 shows the results in terms of a priori aggregated performance. This aggregated performance is calculated as the average of the profitability per contract indicator. In this application case, if the managers consider that scenario 1 or 3 are more likely to happen in a midterm basis, they should apply the interoperable solution given by the option 2. This option can be a good compromise between improvement of the performance and the accessibility of such a scenario Otherwise, in the case that scenario 3 is more likely to happen, they should try to invest in the project recommended by option 3. In such a case, even if the performance considering scenario 2 is in the red part of the comparison matrix, there is a great improvement in both the average aggregated performance and the scenario 2 performance.

These results are obtained from the real case studied in the ISTA3 French Project. They are sufficient to show that a discrete event simulation can help managers to assess their potential performance.

Conclusion and Future Works

This paper presents a method to select in a given context the most appropriate interoperability solution. In order to do so, the first step is the modelling of the collaborative scenarios in order to understand the existing collaboration, if any, and to have a diagnosis on the points to improve. Based on the expected collaboration scenarios, performances of each scenario are assessed through a discrete event simulation approach and an aggregated performance is calculated using a CPMM qualitative model.

In parallel, the accessibility of each scenario is evaluated based on four criteria: human resource, budget, risk and cultural gap.

Finally, the comparison is done for several scenarios in a synthetic decisionsupport matrix in order to select the best solution.

In order to demonstrate the benefits and the applicability of the proposed methodology, a case study was proposed in the last part of the paper related to a real case study.

The main perspective of this work is to develop first a quantitative CPMM model. The difficulty is not high but the number of required data is huge and this is why this kind of quantification is difficult in the domain of interoperability.

The second perspective is to develop a quantitative model to evaluate the accessibility, based on the weighting of the various criteria and aggregation methods.

Fig. 1 .

 1 Fig. 1. Comparison matrix regarding expected performance and accessibility of scenarios.

  to implement each interoperability solution (low, medium, high, super-high) Evaluation of the performance for each option and scenario Assessment of all performances for each option and scenario Evaluation of the global score for each

Fig. 3 .

 3 Fig. 3. Capture of Witness ® Simulation Model SUB1 has to deal with three kinds of CAD files given by MPN:1. Simple files: concern small or simple moulds. These simple files are easily handled by both SUB1 and SUB2, 2. Standard files: concern more complex moulds and represents the most important part of the files received by SUB1, 3. Complex files: concern complex moulds leading to the highest level of disruptions in the process and the highest give-up of the initial order. The simulations are developed according to three interoperability options graded from Low to High in terms of accessibility (see section 3.2):-Option 1 is the most accessible scenario (graded High) in which the improvement of SUB1 interoperability dedicated activities is done through the use of an estimate management system; -Option 2 (graded Medium) is an extension of option 1 to the improvement of SUB2 interoperability dedicated activities in the management of the feasibility study (SUB2 gains access to the estimate management system of SUB1). -Option 3 (graded Low) is an improvement of information transfer through the use of a collaborative platform such as Mediation Information System: this simulates an improvement of interactions for each company.

Fig. 4 .

 4 Fig. 4. Comparison matrix regarding expected performance for the application case

Table 2 :

 2

		Scenario 1		Scenario 2		Scenario 3
	Pis	Opt. 1 Opt. 2 Opt. 3 Opt. 1 Opt. 2 Opt. 3 Opt. 1 Opt. 2 Opt. 3
	Rentability per contract	49%	54%	61%	9%	11%	27%	55%	62%	62%
	Cost of mold production	28	28	28	38	38	38	26	26	26
	Cost of file processing	112	95	78	164	156	136	101	82	83
	Number processed files	1000 1000 1000 1000 1000 1000 1000 1000 1000
	Number of defaults by file	319	336	309	637	662	580	252	235	235
	Number of molds	925	931	921	782	787	782	938	938	938
	Number of defaults by product	244	267	230	419	449	362	190	173	173
	Global lead time with defaults	189	171	143	286	279	229	168	143	143
	Tab. 2. Results given by simulation


Andrea Marino

Pradip Chakraborty

Marina Servol

Maciej Lorenc

Eric Collet

Andreas Hauser
email: andreas.hauser@unige.ch

The role of ligand-field states in the ultrafast photophysical cycle of the prototypical iron(II) spin-crossover compound [Fe(ptz) 6 ](BF 4 ) 2 **

come     The role of ligand-field states in the ultrafast photophysical cycle of the prototypical iron(II) spin-crossover compound [Fe(ptz)6](BF4)2

In 1982 McGarvey and Lawthers reported that the equilibrium between the spin states of iron(II) spin-crossover complexes in solution at around room temperature can be photophysically perturbed via irradiation into the intense spin and parity allowed metal-ligand charge transfer ( 1 MLCT) absorption bands of the low-spin (LS) species. [1] This was followed by the discovery of light-induced excited spin state trapping (LIESST) in the solid state, that is, the population of the high-spin (HS) state as long-lived metastable state at low temperature upon irradiation into the above mentioned 1 MLCT bands as well as into ligand-field (LF) bands. [2] Initially, these effects served to study the HS( 5 T 2 (t 2g 4 e g 2 )) ∏ LS( 1 A 1 (t 2g 6 )) relaxation dynamics in solution [3] as well as in the solid state, where cooperative effects are of interest. [4] Ultrafast pump-probe spectroscopy including structural probes on iron(II) spin-crossover [5] and low-spin complexes [6] in solution with low-lying MLCT states showed that the double intersystem crossing from the initially excited 1 MLCT state to the HS state occurs with quantum efficiencies near unity, takes only ~150 fs, and proceeds via the 3 MLCT state, thus bypassing the low-lying singlet and triplet LF states. For irradiation into the 1 MLCT bands Chang et al. [7] laid the theoretical base for this, and Collet et al. [8] showed that at short delays this sequence of events is also valid for the solid state, that, however, due to the elastic interactions, lattice dynamics result in important after effects. In a recent study on a HS complex in solution at room temperature, Gallé et al. [9] showed that upon irradiation into the weaker 5 MLCT band, the LS state becomes likewise populated through MLCT intersystem crossing.

The role of LF states in transition metal photophysics of d 6 systems such as ruthenium(II) and iron(II) complexes is nevertheless crucial, and that they are by no means innocent is borne out by the discovery of LIESST upon irradiation into the spin-allowed LF absorption bands of the LS species of the spin-crossover compound [Fe(ptz) 6 ](BF 4 ) 2 (ptz = 1propyltetrazole), which has no low-energy MLCT states. [4] In Figure 1 the spin-allowed and the spin-forbidden LF transitions of both the LS and the HS species are assigned. This study also revealed that the thermal relaxation from the trapped HS state sets in at around 50 K, and that at 10 K the trapped system can be pumped back to the LS state by irradiation into the spin allowed LF band of the HS species in the near IR (reverse LIESST). [4] Based on the experimentally determined values of the overall quantum efficiencies of LIESST and reverse-LIESST at 10 K of 0.8 and 0.1 in [Fe(ptz) 6 ](BF 4 ) 2 , respectively, and the fact that LIESST is also observed on irradiation directly into the spin-forbidden transitions of the LS species, the scheme for the different light-induced processes in Figure 2 was proposed, and a value of 4:1 was estimated for the 3 T 1  5 T 2 / 3 T 1  1 A 1 branching ratio at 10 K. [4] For the neat title compound, the near IR and visible spectral region is thus dominated by the weak LF transitions, the rise to the intense MLCT bands being observed only above 30000 cm -1 . The latter can be conveniently studied in a dilute mixed crystal of composition [Zn 1-x Fe x (ptz) 6 ](BF 4 ) 2 , x = 0.01. The corresponding absorption spectrum, included in Figure 1, is strongly temperature dependent. The intense low-temperature band with the absorption maximum at lower energy can be readily assigned to the 1 MLCT transition of the LS species. As the thermal population of the HS state sets in, it looses intensity, till at room temperature it is entirely replaced by the weaker 5 MLCT band of the HS species centred at slightly higher energy. The intensity of the 1 MLCT band at the band maximum thus monitors the HS fraction  HS effectively. Figure 3 shows the thermal spin transition curves with a gradual transition around T 1/2 = 92 K for the dilute system and at T 1/2 = 125 K for the high-symmetry crystallographic phase [10] of the neat title compound. The latter is much steeper due to cooperative effects. [4] LIESST and reverse-LIESST can be used to record HS ∏ LS relaxation curves as shown in Figures 4a andb for irradiation at 488 nm (20500 cm -1 ) and 104 K, and at 830 nm (12050 cm -1 ) and 120 K for [Zn 1-x Fe x (ptz) 6 ](BF 4 ) 2 , x = 0.1, respectively. For the former, the bleaching of the first spin-allowed LF transition of the LS species at 530 nm (18800 cm -1 ) was monitored. For the latter, the transient absorption of the 1 MLCT band at 305 nm (32790 cm -1 ) allowed for a sensitive detection of the light-induced LS population. Figure 4c shows the observed HS ∏ LS relaxation rate constant k obs = k HL + k LH on a logarithmic scale against T -1 determined via LIESST below 120 K and via reverse LIESST from 110 to 180 K in the same system. Above 160 K, the quantum efficiency for reverse-LIESST rapidly drops to zero. The observed relaxation rate constant spans 12 orders of magnitude in the experimentally accessible temperature range. At high temperature the relaxation is thermally activated, whereas at low temperatures it tends towards a quantum mechanical tunnelling process with k obs = k HL (T0) < 10 -6 s -1 . [4] With the above, the optimal conditions for ultrafast pump-probe experiments can be assessed. They were thus performed at 125 K on a mixed crystal with x = 0.1. This temperature was specifically chosen because at 125 K the equilibrium HS fraction is ~85%, and the reverse-LIESST quantum efficiency is still reasonably high, so that pumping at 830 nm can be expected to be as effective as possible. At the same time the HS ∏ LS relaxation occurs within ~0.3 ms allowing one to work at the full repetition rate of 1 kHz of the laser system in order to make use of efficient signal averaging. [8c] For the comparatively high value of x, a very small light-induced LS fraction gives rise to a sizeable signal at the maximum of the intense 1 MLCT absorption. Thus the low absorption cross section at the excitation wavelength is compensated by the high concentration and the sensitivity to the transient population of the LS state at the probe wavelength of 300 nm. Since at 125 K the low-spin fraction is still 15%, the same experimental conditions can be maintained for LIESST irradiation at 530 nm.

Figure 5a shows the kinetic trace of OD at 300 nm following 100 fs irradiation of [Zn 1-x Fe x (ptz) 6 ](BF 4 ) 2 , x = 0.1, at 830 nm, that is, into the spin-allowed 5 T 2  5 E LF transition of the HS state ( 830 = 5 M -1 cm -1 ). Immediately following the excitation pulse, a sharp and strong transient absorption peak is observed, which decays with a time constant of  1 = 1.7( 2) ps (see inset) to a minimum, from which the absorption increases again with a time constant  2 = 39(3) ps. The plateau reached at the end of the rise does not decay within the range of the ultrafast setup. It thus corresponds to the excited state absorption (ESA) of the light-induced population of the LS( 1 A 1 ) state decaying with the above mentioned time constant of 0.3 ms. The 39 ps of the rise to the plateau therefore correspond to the arrival time at the LS( 1 A 1 ) state. The instrumental response function (IRF) of the setup is 150 fs, the decay of the initial signal within 1.7 ps is therefore real and the minimum in the transient signal corresponds to the population of an intermediate state. At the probe wavelength of 300 nm, the vertical 1 MLCT transition from the LS( 1 A 1 ) state has the highest extinction coefficient because this state has the shortest metal-ligand bond length, but as the quantum efficiency of reverse-LIESST is quite low and decreasing with increasing temperature, the amplitude of the plateau corresponding to its light-induced population is not very large. The initially excited state by the laser pulse is the 5 E(t 2g 3 e g 3 ) LF state. In the Franck-Condon state at time zero, its MLCT transition is expected to have an extinction coefficient in the range of the 5 MLCT transition from the HS( 5 T 2 ) state but to occur at lower energy (see Figures 1 and2), that is, at around 30'000 cm -1 , and is thus monitored at the probe wavelength. It decays either via internal conversion back to the HS( 5 T 2 ) state or to the intermediate state. Based on energetic and geometric considerations, the intermediate state of lower energy than the 5 E state can only be the 3 T 1 (t 2g 5 e g 1 ) LF state. [11] The transient signal at very short times thus corresponds to ESA from the hot 5 E state and its fast decay to a combination of vibrational cooling, internal conversion and intersystem crossing. Only the last one will result in the transient ESA at the minimum, and this therefore corresponds to the 3 MLCT absorption from the 3 T 1 , which is spin-allowed and has an extinction coefficient that is intermediate between the ones of the spin-allowed 5 MLCT and 1 MLCT bands from their respective LF states. The 39 ps are much longer than vibrational cooling in the solid state, therefore the second step in the cascade occurs from the thermally relaxed intermediate state.

Figure 5b shows the kinetic trace as OD at 300 nm following 100 fs irradiation of [Zn 1-x Fe x (ptz) 6 ](BF 4 ) 2 , x = 0.1, at 530 nm, that is, into the spin-allowed 1 A 1  1 T 1 LF transition of the LS state ( 530 = 25 M -1 cm -1 ). The ESA signal at t = 0 is attributed to absorption from the hot 1 T 1 state. It decays with a time constant  1 < IRF of the setup, and is replaced by a negative signal. Bleaching must be attributed to the instantaneous depletion of the LS fraction from its equilibrium value of 15% at 125 K, as the LS( 1 A 1 ) state is the most strongly absorbing species present, except for absorption from the hot 1 T 1 state. A second, slower process with a time constant  2 = 1.2(2) ps leads to a still more negative signal, which persists for the duration of the experiment and decays with the time constant of ~0.3 ms of the HS ∏ LS relaxation at 125 K. Does the slower process indicate population of an intermediate state or does it correspond to vibrational cooling in the HS state as the final state of the fast relaxation cascade? Given that (i) the 5 MLCT intensity at the probe wavelength is much lower than the 1 MLCT intensity, (ii) 3 MLCT intensities from triplet states are expected to be in between the two, and (iii) the overall quantum efficiency of the light-induced LSHS conversion is high, the former is more probable. However, the 1.2 ps, are much shorter than the 39 ps attributed to the lifetime of the 3 T 1 state in reverse-LIESST, and therefore this state cannot be the intermediate state for LIESST upon LF excitation. According to Ordejon et al. [11] direct 1 T 1  5 T 2 intersystem crossing with S = 2 is unlikely because of very weak spin-orbit coupling between these two states. But spin-orbit coupling in conjunction with vibronic coupling to a non-totally symmetric mode couples the higher-energy 3 T 2 state quite strongly, and indeed more strongly than the 3 T 1 state, to the 1 T 1 state. [11] The 3 T 2 state, in turn, is strongly coupled to the 5 T 2 state, and thus it is the natural candidate as intermediate state for LIESST via LF excitation. Do the above results verify the picture proposed in Ref. [4] or does it need modifying? Qualitatively the picture remains valid, the low-lying triplet LF states do play a role in the photophysical cycle of [Fe(ptz) 6 ](BF 4 ) 2 , and at least for reverse-LIESST, the double intersystem crossing is sequential. The individual quantum efficiencies, and possibly the branching ratio at the 3 T 1 state given in that reference may need to be revised. These were derived based on the observation of overall quantum efficiencies and the assumption that all intersystem crossing processes follow Fermi's Golden Rule, that is, that vibrational cooling in each state is faster than its lifetime, and that therefore its fate is not influenced by the way it is populated. This is correct for the 3 T 1 state when populated with little excess energy via reverse-LIESST, that is, from the 5 E state upon 5 T 2  5 E excitation. Its lifetime is longer than vibrational cooling, and the branching ratio is expected to follow the semi-classical behaviour of a non-adiabatic multi-phonon process occurring between two well-defined Born-Oppenheimer states, [12] as also found for the HSLS relaxation itself. The fact that the action spectrum for reverse-LIESST follows the 5 T 2  5 E absorption band, [4] indicates that the probabilities for the first step are likewise well-defined. This is no longer the case for irradiation into the spin-allowed 1 A 1  1 T 1 LF transition of the LS species. The relaxation from the initially excited 1 T 1 to the 5 T 2 state is as fast as for excitation into the 1 MLCT bands in the above-mentioned systems. Vibronic coupling between the excited states leads to a breakdown of the Born-Oppenheimer approximation. The electronic and the nuclear wave functions are strongly coupled during the process. The triplet state(s) cannot be identified as true intermediate states, they only serve as mediators dynamically mixed into the electronic function as the system evolves. For a full-scale study we will expand our investigations to different probe wavelengths in the UV, which will allow a more quantitative evaluation of the data, and we will study the temperature dependence of the relevant processes in the present system as well as related systems.

In conclusion, we have investigated the role of the LF states in the photophysical cycle of iron(II) spin-crossover complexes. As for irradiation into MLCT states, the intersystem crossing processes upon irradiation into LF states are ultrafast. These findings are of general importance for the photophysics of transition metal compounds, for instance in comparison with the much studied chromium(III) complexes, [13] or for ruthenium(II) complexes being used in photovoltaic devices [14] or in cancer phototherapy. [15] With regard to the latter, it is interesting to note that in [Ru(6-methyl-2,2'bipyridine) 3 ] 2+ the corresponding 3 T 1 state has recently been located as intermediate state in the ultrafast quenching of the 3 MLCT luminescence, the 3 T 1 state itself having a lifetime of 450 ps. [16] Experimental Section [Fe(ptz)6](BF4)2 and [Zn1-xFex(ptz)6](BF4)2, x = 0.01 and 0.1, were prepared and hexagonal crystals (~330.2 mm 3 ) were grown as described in Ref. [17]. Variable temperature single crystal absorption spectra were recorded on a Cary 5000 spectrometer with the sample mounted on the cold finger of a closed cycle cryosystem (Janis-Sumitomo) capable of achieving temperatures down to 4 K. Irradiation experiments and HS ∏ LS relaxation measurements on timescales from nanosecond to days were performed as described in Ref. [4]. For reverse-LIESST experiments at T > 120 K, 830 nm light from an OPO (Opotek-Magic Prism) pumped by the third harmonic of a Nd:YAG laser (Quantel Brillant) was used. Ultrafast pump-probe experiments on a crystal of [Zn1-xFex(ptz)6](BF4)2, x = 0.1, were performed as described in Ref.

[8c] with 5 J pulse energy focused to ~200 m for pumping and < 0.1 J focused to ~50 m for probing. The sample temperature was controlled with a N2 cryocooler (Oxford Instruments Cryojet). Data treatment involved iterative fitting of a double exponential test function convoluted with a Gaussian IRF function of 150 fs FWHM. ), both monitored at 300 nm (33330 cm -1

). In b) the decomposition of the contributions to the transient signal is indicated schematically.

Figure 1 .

 1 Figure 1. Single crystal absorption spectra of [Fe(ptz)6](BF4)2 at 10 K (-), 295 K (---) and after irradiation at 530 nm (-) with the assignment of LF transitions in the LS and the HS state (left axisadapted from Ref. [4]). Variable temperature (10 K intervals) absorption spectra of [Zn1-xFex(ptz)6](BF4)2, x = 0.01, in the region of the MLCT transitions (right axis).

Figure 2 .

 2 Figure 2. Schematic representation of the electronic structure of iron(II) spin-crossover compounds with only high-energy MLCT states. LIESST (ex = 530 nm) and reverse-LIESST (ex = 830 nm) via the LF states as in [Fe(ptz)6](BF4)2 are indicated by curly arrows. The 305 nm probe (---) monitors the MLCT transitions.

Figure 3 .

 3 Figure 3. Spin transition curves for [Fe(ptz)6](BF4)2 in the crystallographic high-temperature phase (), and in [Zn1-xFex(ptz)6](BF4)2, x = 0.01 ().

Figure 4 .

 4 Figure 4. The HS ∏ LS relaxation in [Zn1-xFex(ptz)6](BF4)2, x = 0.1: a) transient absorption at 530 nm for ex = 488 nm at 104 K (LIESST); b) transient absorption at 305 nm for ex = 830 nm and 120 K (reverse-LIESST); c) observed relaxation rate constant kobs = kHL + kLH vs. T -1 on a logarithmic scale, () ex = 488 nm (taken from Ref. [4]) and () ex = 830 nm.

Figure 5 .

 5 Figure 5. Ultrafast transient absorption profiles for [Zn1-xFex(ptz)6](BF4)2, x = 0.1, at 125 K for a) ex = 830 nm (12050 cm -1 ), and b) ex = 530 nm (18800 cm -1

These authors contributed equally to this work. This work was financially supported by the Swiss National Science Foundation (Grant No. 200020_137567), the CNRS, Région Bretagne, the ANR (09-BLAN-0212), and Europe (FEDER).


Vladimir Y Zaitsev

Vitali Goussev

Vincent Tournat

Patrick Richard

V E Gusev

Slow Relaxation and Aging Phenomena at the Nanoscale in Granular Materials

Keywords: numbers: 83.80.Fg, 43.25.+y, 45.70.-n, 83.10.Tv

come   L'archive ouverte pluridisciplinaire

Introduction.-Slow relaxation phenomena in granular systems are of considerable interest to understand the physics of complex glassy-type systems [1], for which they act as macroscopic analogs of ensembles of atoms and molecules [START_REF] Richard | [END_REF]. Granular systems are also crucial in many industrial and geophysical applications. Particularly, sufficiently ample understanding of nonlinear dynamics of individual contacts is required to interpret such intriguing and poorly understood phenomena as triggering of earthquakes by elastic waves with amplitudes significantly smaller than the damage threshold for rocks [3,4]. Compared to the widely studied slow macroscopic (i.e., grain-scale) rearrangements causing compaction of granular materials [START_REF] Richard | [END_REF][5][6][7][8], processes at nanoscale potentially driven by weak strains, including natural thermal fluctuations, are much less studied. The latter are reasonably believed irrelevant to grain rearrangements during compaction and jamming-unjamming transitions [START_REF] Richard | [END_REF]9]. However, using appropriate acoustic techniques, spontaneous thermally activated nanoscale processes can also be macroscopically observed. In particular, observations of slow relaxation of the elastic modulus in laboratory samples with cemented granular structure [10] as well as similar effects in field measurements in sandy soil on a scale of ∼ 10 m [11] are known. High-intensity acoustic "conditioning" [10] or a mechanical impact [11] ruptured the weakest bonds and produced perturbations in the elastic moduli of order 10 -6 -10 -3 that were rather problematic to monitor. To overcome this experimental difficulty, a parameter dominated by the weak-bond-network rather than the stable material skeleton is highly desirable. Here, we report (i) implementation of such an unconventional experimental approach, (ii) a model of individualcontact bistability having essentially new features compared with conventional ones discussed for AFM tips and adhesion hysteresis, and (iii) results of numerical simulations of collective behavior of such bistable contacts. These results capture essential observed features, in par-ticular, the abrupt breaking of the nanoscale contacts, their slow post-shock restoration and the peculiar aging of the system, and the damage accumulation produced by repeated weak perturbations.

Methods.-Experimentally, we use an acoustic (usually P -wave) component produced by the own material nonlinearity, which is strongly dominated by the contributions of the weakest-contact fraction [12,13]. Thus, amplitude variations of the nonlinear component, characterize temporal variations in the amount of contributing weak contacts. Compared with intact homogeneous solids, nonlinearity of granular packings is giant and can be observed much easier. Feasibility of such nonlinearacoustic sounding was demonstrated in Ref. [14] using the nonlinear cross-modulation technique to monitor structural perturbations in granular material bulk induced by weak mechanical shocks. Another, practically simpler, nonlinear-demodulation technique was successfully applied for studying fine structural changes -avalanche precursors-in slowly tilted granular packings [15,16].

Here, the sounding technique [15,16], combined with pulse-type perturbations [14], is used to study slow relaxation of the weak-bond network in granular material with particular attention to aging of material undergoing repeated perturbations [16]. We use random packings of glass beads 1 and 2 mm in diameter placed in a container 5 -10 l in volume, to which a small electromagnetic shaker is attached. It produces perturbing pulses that are much weaker compared to typical conditions of tap-induced compaction [START_REF] Richard | [END_REF][5][6][7] and surely do not cause macroscopic grain rearrangements. The strain amplitude of the pulses varied in different measurements from about 10 -7 to 10 -6 and their duration is 20 ms. The primary amplitude modulated wave is at strain amplitude εA ∼ 10 -8 -10 -7 (see also Ref. [17]). Unlike observations of the primary wave [10,11] dominated by the medium skeleton, we use the demodulated component that is strongly dominated by the weakest contacts in the material. This is confirmed by the fact that such moderate shocks with nanometer and even subnanometer displacements, which are able to break only the weakest contacts, can cause several-times drops in the demodulated-component amplitude. Thus, such drops are proportional to the number of shock-ruptured weak contacts (see also Ref. [15]), and the slow relaxation of the nonlinear-component amplitude reflects how those contacts are restored.

Figure 1 shows examples of slow relaxation in granular materials, observed via the amplitude of their nonlinearacoustic response. If time t is counted from the shock endings, the latter amplitude demonstrates power-law rates close to 1/t 1+n with |n| ≪ 1, i.e., close to logtime behavior corresponding to n = 0. Plots (a) and (c) demonstrate peculiar weakening of the material reaction to series of identical taps, i.e., a kind of "aging." Besides, plots (a) and (b) show that the nonlinearityproduced signal is much more sensitive to the state of weakest contacts than the fundamental component variability. Concerning the gradual relaxation of the shockinduced perturbations, we note that even if the probing signal is switched off just after the shock and switched on after a pause, the nonlinearity of the material restores spontaneously. This shows that the influence of the probing wave does not dominate the effect, although high-intensity acoustic strains (say 10 -5 ) may perturb the weak bonds [10,17,18].

Mechanism.-Under room temperature T ∼ 300 K the characteristic thermal energy k B T (k B being the Boltz- Rigid cantilever, one equilibrium

Bistability zone unstable point

Tensile elastic force induced in asperity by adhesion mann constant) unambiguously indicates that thermal fluctuations cannot affect the state of visible, even weakly loaded, macroscopic contacts usually considered in granular matter modeling [9,19]. Thus only nanoscale surface asperities (from tens to hundreds of nanometers) can be considered as candidates of bistable structural elements potentially sensitive to thermal fluctuations. To understand the origin of their bistability, the analogy with the bistable behavior of tips in atomic-force microscopy (AFM) is very useful. For a tip already compressed by the contacting solid, the Hertzian force is repulsive, whereas the tip yet approaching a solid surface experiences the influence of short-range attraction forces. This attraction force for an AFM tip approaching another solid is equilibrated by the elasticity of the cantilever [dashed lines in Fig. 2(a)]. If the cantilever is soft enough, a bistability zone for the initial position A 1 ≤ A ≤ A 2 of the unstressed cantilever can appear [START_REF] Burnham | Surface Forces and Adhesion[END_REF] as illustrated in Fig. 2(a). In this zone, the cantilever can equilibrate the attraction force at two positions of the tip, "closed" and "open." Note that, in the latter position, the attraction force is almost absent. If the cantilever is moved forth and back, peculiar hysteretic jumps between the two positions occur [arrows in Fig. 2(a)]. Inside the bistability zone sufficiently strong thermal fluctuations can cause transitions between the two equilibrium states.

2 / 1 x F adh ∝ 2 / 3 | | x ∝ "open" contact "closed" contact

Soft cantilever, potential bistability

A 1 A 2 Force / 10 -7 N 012 012 012 a d A 8 . 1 = a d A 9 . 1 = a d A 96 . 1 = Energy, a.u. E b E c E b,c / 100k B T E b E c r = 30 nm r = 100 nm (a) (b) (c) (d) x/d a A A x/
At first glance, for nanoscale asperities at grain surfaces, there is no "soft cantilever" to create bistable equilibria like in AFM. However, as argued in Ref. [START_REF] Johnson | Contact Mechanics[END_REF], the elastic energy stored in compressed contacts scales like h 5/2 , h being the displacement of the contact apex. Accordingly, the elastic force F comp follows the Hertzian law F comp ∝ h 3/2 . But the same arguments applied to a contact apex displaced by the value |h| = |x -A| due to a localized attractive force also lead to the appearance of an elastic force F tens ∝ |x -A| 3/2 that equilibrates the attraction [dash-dotted curves in Fig. 2(b)]. Unlike AFM cantilever elasticity, this elastic force is nonlinear; i.e., initially it can be sufficiently soft to create the second (distant) equilibrium position for the contact tip. For AFM tips with the typical radius r < ∼ 10 nm, however, this "nonlinear spring" hidden inside the tip is insufficiently soft relative to adhesion, so that only an in-sequence connected soft cantilever can create the second potential minimum. But for a larger contact radius r > ∼ 30-50 nm, due to a different dependence on r for the attraction and the "hidden spring", the latter becomes sufficiently soft relative to the adhesion force [compare the curves for r = 30 nm and r = 200 nm in Fig. 2(b)]. Thus, for the larger contacts, bistable equilibria can appear in a finite range of separations between the asperity apex and the opposite surface without the necessity of an artificial soft spring or cantilever. Figure 2(c) schematically shows how the resulting two-minima potential evolves with the initial separation A. These representations suggest physically clear interpretation to the well-known [START_REF] Deryagin | Surface forces[END_REF] transition from the so-called Derjaguin-Muller-Toporov (DMT) model of very small contacts not having bistability to the Johnson-Kendall-Roberts (JKR) model for larger contacts exhibiting adhesion hysteresis [START_REF] Deryagin | Surface forces[END_REF]. The latter can be viewed as a special case of mechanical hysteresis, like for AFM tips, but arising without an artificial soft cantilever.

For elastic and surface energy typical of glasslike materials, contacts with r ∼ 10 2 nm and T ∼ 300K exhibit narrow regions near the boundaries of the bistability zone, where one of the potential wells [E b or E c , see Fig. 2(b)] is 10 2 to 10 4 times larger than k B T , while the other is of order 10 1 k B T . Thus, near the left boundary of the bistability region the closed state is much stabler, whereas the open one is metastable. Near the right boundary, the situation is the opposite. The metastable equilibrium energy is comparable with that of thermal fluctuations. So, they are able to induce jumps to the opposite stabler state with characteristic waiting times τ 0 exp(E b,c /k B T ) according to the Arrhenius law, where the attempt time for nanometer-scale tips of the asperities can reasonably be τ 0 ∼ 10 -12 s.

Direct AFM inspection of the glass-bead surfaces confirmed the presence of numerous asperities about 10 2 nm in radius and 20-50nm in height (see Ref. [23]) consistent with the values reported in [START_REF] Divoux | [END_REF]. A single macrocontact between two grains leads to 10 3 -10 4 microasperities. Even if 1% of them actually get in contact, one obtains ∼ 10 2 of such nanoscale contacts for a visible one. Following Refs. [13,15] we conclude that contribution of such loose but numerous nanocontacts can dominate over the nonlinearity of much stronger (and thus less nonlinear) macrocontacts creating the material skeleton. This explains why nonlinearity can drop drastically after fairly weak shocks that still leave the material skeleton intact, but suffice to break the nanocontacts.

Contour arrows in Fig. 2(d) schematically show the physical meaning of the relaxational closing of open contacts and the destructive action of perturbing weak tensile shocks, which do not completely get the system out of the bistability region. We recall that even for large nanocontacts (with r > ∼ 10 2 nm), the bistality zone is of order of atomic size. Note that for characteristic attempt times τ 0 ∼ 10 -12 s and waiting times below tens of hours, only "active" contacts with barriers < ∼ 45k B T can participate in thermally induced transitions. Then the narrow "active" parts of the energy curves near the bistability-region boundaries can be fairly well approximated by straight segments [thick solid lines in Fig. 2(d)]. Consequently, in such narrow regions for almost arbitrary distributions of the asperities' heights, the density of energy states for the active nanocontacts can be approximated as constant.

Kinetic Monte Carlo approach.-Using a kinetic Monte Carlo approach, we simulated transitions between "open" or "closed" states [see Figs. , but then the closing front continues its movement to the right. For the same shock duration and amplitude, the resulting amount of the broken contacts that increases N b (E) essentially depends on the position of the closing front just before the shock (compare the upper and lower rows in Fig. 3). Even stronger perturbations can already shift all bistable contacts to the right beyond the bistability zone and break all earlier closed contacts. Since the width of the bistability zone is of the order of an atomic size, such strong shocks correspond to strains > ∼ 10 -6 -10 -5 for millimetric grains. For weaker shocks, the system response can be rather multivariant depending on shock amplitude, duration, and previous history. For example, besides the difference in the amounts of broken contacts, Fig. 3(b) shows that, by the same post-shock relaxation time, the closing front (curve 3) gets already to the right from its initial position [curve 1 in Fig. 3(b)] in contrast to the opposite situation in Fig. 3(d). Next, let us recall that besides the difference in the barrier energies E b,c the widths of bistability zones can strongly differ for different contact sizes. Depending on that width, the same perturbation can be "strong" or "weak," so that perturbation or relaxation regimes for such fractions of bistable elements are quite different.

T k E B / 23 1 (b) closing breaking 1 2 3 (a) 2 3 1 (c) 1 2 3 (d)
For the discussed features, the "aging" of the relaxation response to repeated weak shocks breaking small contact portions is a natural consequence. Such multiple weak shocks applied to previously well-relaxed material [like in Figs.

b (E) -N

b (E) strongly exceeds N ever, that state, for which the relaxed front 3 gets to the right from the initial position 1, is not reached and the system response saturates when the relaxation between the shocks becomes able to heal the perturbation ∆N b produced by every previous shock. This saturated value ∆N b is significantly smaller than the initial reaction of the well-relaxed system to the first perturbing impact. The transition to such "aged" reaction of the system is shown in Fig. 4 for the simplest situation of identical nanoscale contacts for which the barriers differ only by initial separation A. This model fairly well reproduces the observed gradual "aging" of the system response to repeated weak shocks [see Fig. 1(c)].

Discussion and conclusions.-Even without externally applied shocks, the discussed mechanism of nanocontact destruction or restoration manifests itself in slowly tilted granular packings [15,16], where the avalanche precursors act as internal "shocks" followed by relaxations [see inset in Fig. 1(b)]. For periodical forth-and-back tilting below the critical angle, the demodulated-signal variations strongly decrease (become "aged"). However, after ∼ 1 hour rest, during which the broken nanocontacts restore, the signal variations also significantly restore [16].

Above we focused on fairly weak perturbations, after which the contacts relax independently of each other. If a stronger shock breaks a significant portion of nanocontacts, the surfaces of macroscopic intergranular contacts can experience separation even greater than individual bistability-zone widths. Then the interstate jumps of nanocontacts are not independent, and really collective hysteretic or relaxational mechanisms become important as will be discussed elsewhere. But even for weak perturbations, the revealed mechanism demonstrates a rich variety of regimes, including the aging [1] that has a rather general nature. The considered bistability of nanoscale contacts is a universal feature of both nonconsolidated (sand-like) and cemented (sandstone-like) granular materials, as well as solids with cracks having contacts at their interfaces. This explains universality of slow-dynamics effects observed in those materials [3,10,11,[14][15][16][START_REF] Guyer | Nonlinear Mesoscopic Elasticity[END_REF]. Understanding of the gradual accumulation of broken contacts due to multiple weak perturbations, like in Fig. 4(a), opens prospects for physical interpretation of such intriguing phenomena as dynamic earthquake triggering that is phenomenologically discussed in Ref. [3] and the influence of fairly weak seismo-acoustic stimulation on oil recovery from nearly depleted wells [START_REF] Beresnev | [END_REF].

Support of ANR Grant No. 2010-BLAN-0927-01 and Grant No. 11.G34.31.0066 of the Russian Federation Government is acknowledged. V.Z. acknowledges the invited-professor grant from the University Rennes-1. We thank J-F. Bardeau for the help with AFM imaging.

1 A

 1 FIG. 2. (color online). Schematic elucidation of the contactbistability origin. (a) Adhesion or compression force (solid line) for a small asperity (r = 30 nm) and equilibrating elastic force of a cantilever (dashed lines) which jointly are able to produce bistable equilibria if the cantilever is soft enough (the most-right and most-left intersection points). The elastic parameters and surface energy used are those of glass. (b) Elucidation that Hertzian-like elastic tensile force for sufficiently large contacts subjected to short-range adhesion forces from an opposite solid surface can also form bistable equilibria. (c) Corresponding two-minimum potential wells, for which the energy barriers E b,c exhibit opposite trends as a function of separation A normalized to atomic size da. (d) Energy barriers E b (A) and Ec(A) that should be overcome to break "closed" contacts and close "open" ones. Dashed rectangles show low-energy regions in which thermal fluctuations can induce jumps to the opposite equilibrium.

  2(b) and 2(d)] for 3×10 4 contacts. The probabilities of interstate jumps are given by the aforementioned Arrhenius law. If initially all nanoscale contacts are broken, the broken-contact density N b (E) = 1 and population of closed contacts is zero, N c (E) = 0. Gradual closing of the broken contacts starts from smallest energy barriers and looks as the motion of the steplike curve N b (E) -"closing front" -towards the right boundary of the bistability zone with larger barriers. As argued above, the nonlinear-signal amplitude is proportional to the number of closed nano-contacts N c (E)dE. Curves 1 in Figs. 3(b) and 3(d) show the closing front positions after s and 1500 s of the initial relaxation, respectively. For contacts corresponding to the current position of the relaxation front that moves from the left boundary of the bistability zone to the right [Figs. 3(c) and 3(d), curves 1], the energy wells are deep for the open states and shallow for closed ones [see Fig. 2(d), left side]. Sufficiently strong tensile perturbations temporarily shift the nanocontacts towards the right boundary of the energy diagram where, in contrast, energy wells for closed states are shallow [Fig. 2(d), right side]. Consequently, transitions of previously closed contacts back to open states are fostered. As a result, at the end of a shock, the preshock position of the closing front [Figs. 3(b) and 3(d), curves 1] is shifted back to the

Number of closed contacts / 10 3 FIG. 3 .

 33 FIG. 3. (color online). Evolution of the number of closed nano-scale contacts (left) and populations N b (E) of broken ones (right). Upper and lower rows are for the just prepared packing with N b (E) = 1 relaxed during 30 s and 1500 s, respectively. In both cases the same fairly weak perturbing shock that breaks only a portion of earlier closed contacts is applied. Labels 1 and 2 are for the system state just before and just after the shock. Labels 3 are for the system states 24 s after the shock. Compare experimental Fig.1(d)with Fig.3(a), where the dashed curve shows continuous relaxation. Note the much smaller difference between states 2 and 1 for the initial relaxation time 30 s [(a) and (b)] than for 1500 s [(c) and (d)].

FIG. 4 .

 4 FIG. 4. (color online). Simulated "aging" of reaction to multiple weak shocks with accumulation of broken contacts for a well relaxed (during 3 × 10 3 s) system. (a) is the time-domain representation similar to the experimental Fig. 1(c); (b) and (c) are the energy spectra of broken contacts. The mutuallycorresponding moments in plots (a), (b), and (c) are marked by the same numbers. Dashed lines in plots (b) and (c) show that initial perturbation N

  in the "aged" state, and the "aged" relaxed spectra N