Benjamin Camus
email: benjamin.camus@loria.fr

Virginie Galtier
email: virginie.galtier@centralesupelec.fr

Mathieu Caujolle
email: mathieu.caujolle@edf.fr

Hybrid Co-simulation of FMUs using DEV&DESS in MECSYCO

Keywords: co-simulation, hybrid model, DEVS, DEV&DESS, FMI ACM Classification I.6.1 SIMULATION AND MODELING: (e.g. Model Development)

Co-simulation is a key tool in the design and operation of a growing number of complex cyber-systems. But efficiently yet accurately combining continuous time components (such as FMUs) with event-based ones can be challenging, both from a modeling perspective and an operational, tools-oriented one. We propose a platform to tackle this problem building up on MECSYCO, a MAS-based DEVS wrapping platform dedicated to co-simulation. Relying on the ability of DEVS to integrate the DEV&DESS formalism -which offers a sound framework for describing hybrid models-we propose a DEV&DESS wrapper for FMU. This wrapper encapsulates a version of the DEV&DESS simulation algorithm for FMU components which is notably composed of: (1) a forecast strategy which searches for the next state-event;

(2) a bisectional algorithm to approach the location of the state-change in an FMU. Our solution is implemented using Java and JavaFMI to control the FMU. Our sample case is the co-simulation of a barrel-filler factory implemented in different FMUs and event-based models. Compared to related works, our proposal is functional, generic, yet evolutionary, and benefits from the strong foundations of DEV&DESS.

INTRODUCTION

Within the next two decades the electrical distribution grids will undergo large transformations with the massive connection of intermittent energy resources (wind and solar generation) at Low and Medium Voltage levels, as well as the development of new usages such as electric vehicles charging. These evolutions burst the need for new functions, tools and communication media to be integrated in the Distribution Management System (DMS) of the Distribution System Operators (DSO), making the power grids "smarter".

These evolutions introduce a new level of complexity when studying the resulting system: the proactive management of the Smart Grids requires that domains such as telecommunication and information systems should be considered in addition to the "classical" electrical world. And, because of the strong interactions existing between these domains, considering each domain separately becomes no longer sufficient to picture an accurate state of the whole system. Real testbeds are a necessary stage before experimenting on the field, but they are time and cost consuming and provide limited insight regarding large scale deployment.

A solution to this problematic thus lies in co-simulation. Cosimulation consists in performing a simulation by reusing models executed in different pre-existing simulation software. It allows each specialist involved in a complex system to keep using the tools which are popular in his/her community (for instance NS-3 for telecommunication networks specialists, Dymola for physics and control specialists, EMTP-RV for electromagnetic specialists...) while providing to each of them a realistic context. In addition, each simulator can (in some cases) execute on a different machine, which makes possible the co-simulation of very large systems. The challenge is to ensure interoperation of rather stand-alone tools: to synchronize the execution of the simulators, and to perform actual exchange of simulation data among them. FMI (Functional Mock-Up Interface) [3] establishes itself as a standard for model exchange and co-simulation of equational models. It enforces some generic rules and a software interface to manipulate equational models and their numerical solver. Building on that interface, any equational component can be embedded into an FMU (Functional Mock-up Unit) helping to solve the interoperability problem for the cosimulation of equational models. The numerical resolution of a system can then be performed by defining a set of communication points between the FMUs according to a trade-off between the accuracy of the simulation results and the performances of the co-simulation process.

In the context of the modeling and simulation (M&S) of complex cyber-systems such as Smart Grids, the FMU components must interact with models written in others formalisms -such as event-based ones-within a multi-paradigm [START_REF] Zeigler | Multifaceted, multiparadigm modeling perspectives: tools for the 90's[END_REF][START_REF] Vangheluwe | An introduction to multi-paradigm modelling and simulation[END_REF] co-simulation. The issues faced are then related to hybrid modelling [START_REF] Cellier | Combined continuous/discrete system simulation languages-usefulness, experiences and future development[END_REF] where discrete and continuous formalisms are combined: in order to manage the FMU execution, we need to deal with event occurrences in addition to the communica-tion points of the equations numerical resolution. However, as it focuses on the software API level, FMI does not offer a solution to this integration need. Thus, in order to obtain a generic solution, a sound framework for describing hybrid co-simulation with FMUs is needed.

We show in this article that, thanks to its integrative power [START_REF] Vangheluwe | An introduction to multi-paradigm modelling and simulation[END_REF] and its capacity to embed the DEV&DESS hybrid system formalism, the Discrete EVent System specification (DEVS) fullfils this requirement. Our contribution consists in specifying a DEVS wrapper for hybrid co-simulation of FMU components by relying on DEV&DESS. As an FMU offers a limited control whereas DEV&DESS does not make hypothesis on the equational models manipulation, we propose to adapt the DEV&DESS simulation protocol in this wrapper. We implement this proposal in MECSYCO, our DEVS wrapping platform.

The article is articulated as follows. Section 2 describes a simple yet representative example of an hybrid system and details the issues raised by co-simulation. Section 3 presents DEVS and how it enables hybrid modelling, and describes MECSYCO. Section 4 constitutes the center of our contribution as it describes our DEVS wrapper for FMU components. Section 5 presents the implementation of our solution and the simulation results for our use-case. Section 6 positions our proposition with regards to related works. Section 7 summarizes our contribution and lists perspectives.

USE-CASE

We present here the case of a barrel-filler factory (inspired from [START_REF] Praehofer | System theoretic formalisms for combined discrete-continuous system simulation[END_REF]) composed of four parts (Figure 1) detailed below. This example was chosen for an explanatory purpose, but also to illustrate that our work is generic and can be applied outside from the complex context of the Smart Grids.

• A queue of barrels waiting on a conveyor to be filled. The factory fills only one barrel at a time. As soon as the water reaches a given level in the barrel, the barrel is carried away by the conveyor, and the filling process starts again for the next empty barrel.

• A tank storing the water to fill the barrels. The flow rate of water filling the barrel decreases with the level of water in the tank.

• A controller c1 manages the opening of the valve between the tank and the barrel. The valve can only be in two states "open" (water goes from the tank to the barrel) or "close" (the filling process is stopped).

• A controller c2 regulates the whole filling process. It can change the target level of the barrels, and abort the current barrel filling. In the former case, when the command is received, the factory takes into account the new target level only after the current barrel has reached the previous target level. In the latter case, after a short reaction delay the current barrel is carried away and another barrel is filled.

To illustrate hybrid simulation, we choose to model the factory as a combination of continuous (the water flow from the tank to the barrels) and discrete (changes of barrel and controllers commands) dynamics. We use four models to describe the factory functioning.

Two event-based models describe the discrete dynamics. These models send commands at predefined dates. The c1 model sends "open"/"close" events through its valve output port in order to control the barrels water supply. The c2 model has two output ports, abort and size, used respectively to abort the current barrel filling and to change the target level of the barrels.

Two equational models are used to describe the continuous dynamics. These models are separately defined in Modelica using block diagrams, and exported from Dymola as FMUs for co-simulation according to FMI 2.0 standard. The tank model (Figure 2) describes, according to the valve status, the evolution of the level of water in the tank, and the resulting output flow rate. The barrel model (Figure 3) describes the evolution of the level of water in the current barrel, according to the input flow rate.

This example illustrates that the continuous component must define within all its continuous states, some states which are meaningful for the event-oriented world. For instance a barrel can be empty, filling or target reached. The change from filling to target reached constitutes a "state event" [START_REF] Cellier | Combined continuous/discrete system simulation languages-usefulness, experiences and future development[END_REF]. In a classic FMU-based co-simulation, each FMU executes independently and FMUs exchange simulation data at pre-determined instants of communication. The frequency of these communications is chosen according to a performance-accuracy tradeoff. From a model point of view, it is obvious that when a state event occurs, it is important that the continuous component immediately informs the event-based world; otherwise, simulation would skew the factory behaviour: the factory will keep filling the barrel for a while after the target level is reached. As a consequence, the result of the simulation -the number of barrels produced by the factory -will be inaccurate: it will be less than what the tank volume would allow in the real factory. Reciprocally, when the continuous model (the barrel) receives a command (for instance "abort") from the control system, it must take it into account immediately in conformance with the model: if after the reaction delay, the barrel keeps filling up for a while, the result of simulation will again be inaccurate.

But with an FMU-based co-simulation, these two actions are not done so easily since :

• state events occuring between 2 points of communication are localized at the upper communication point, pending improvements of the hybrid-cosimulation in the FMI standard.

• new inputs are only taken into account at the next communication point no matter when they are received (the abort orders are only applied at the communication points).

An effort is thus required to integrate the operational software in such a way as to respond to events. In addition, this integration should be as generic as possible since this example is for illustration purposes only and the solution we propose applies in a broader context.

MULTI-PARADIGM M&S WITH A DEVS WRAPPING PLATFORM

The DEVS Formalism

DEVS [START_REF] Zeigler | Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems[END_REF] is an event-based formalism for the M&S of system of systems. One important feature of DEVS is its universality which positions it as a pivot formalism for multiparadigm modelling and simulation [START_REF] Vangheluwe | DEVS as a common denominator for multi-formalism hybrid systems modelling[END_REF]. Indeed, not only DEVS appears to be universal for describing discrete-event systems [START_REF] Zeigler | Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems[END_REF], but it can also integrate continuous systems [2] expressed for instance with differential equations [START_REF] Quesnel | DEVS coupling of spatial and ordinary differential equations: VLE framework[END_REF]. Of particular interest in the scope of this article is the fact that, as shown by [START_REF] Zeigler | Embedding DEV&DESS in DEVS[END_REF], DEVS can also embed the DEV&DESS formalism [START_REF] Praehofer | System theoretic formalisms for combined discrete-continuous system simulation[END_REF]. This formalism offers a sound framework for describing hybrid systems as it describes how continuous systems interact and co-evolve with the discrete world.

As summarized by [START_REF] Quesnel | DEVS coupling of spatial and ordinary differential equations: VLE framework[END_REF], the integration of a formalism in DEVS can be performed either by a mapping or a wrapping. While the former consists in establishing the equivalence between the formalisms, the latter implies bridging the gap between the two abstract simulators [START_REF] Kim | A heterogeneous simulation framework based on the DEVS BUS and the high level architecture[END_REF]. The advantage of the wrapping strategy is to enable reusing pre-existing models already implemented in some simulation software [START_REF] Mittal | A system-of-systems approach for integrated energy systems modeling and simulation[END_REF]. Once integrated in DEVS, different heterogeneous models can be co-simulated using a common simulation protocol: the sequential or the parallel DEVS one. Thanks to its integrative power, DEVS constitutes a strong base for the M&S of complex cyber-systems.

The Figure 4 shows a DEVS view of our barrel-filler factory example. Each model corresponds to a DEVS atomic model. Together, these atomic models describe the behaviour of the system, and the whole barrel-filler factory is represented by a DEVS coupled model which describes the structure of the system (i.e. how the atomic models are interconnected).

Presentation of MECSYCO

A Multi-agent Environment for M&S MECSYCO (Multi-agent Environment for Complex SYstem CO-simulation) [START_REF] Camus | Combining DEVS with multi-agent concepts to design and simulate multi-models of complex systems (WIP)[END_REF] is a DEVS wrapping platform that takes advantage of the DEVS universality for enabling multiparadigm co-simulation of complex systems. As shown in previous work [START_REF] Camus | Considering a multi-level model as a society of interacting models: Application to a collective motion example[END_REF], the platform also supports multi-level modeling. It is currently used for the M&S of smart electrical grids in the context of a partnership between Inria (French IT research institute) and EDF R&D (leading French electric utility company) [START_REF] Vaubourg | Multi-agent multi-model simulation of smart grids in the MS4SG project[END_REF].

MECSYCO is based on the AA4MM (Agents & Artifacts for Multi-Modeling) paradigm [START_REF] Siebert | Agents and artefacts for multiple models co-evolution: building complex system simulation as a set of interacting models[END_REF] that sees an heterogeneous co-simulation as a multi-agent system. Within this scope, each couple model/simulator corresponds to an agent, and the data exchanges between the simulators correspond to the interactions between the agents. Originality with regard to other multi-agent multi-model approaches is to consider the interactions in an indirect way thanks to the concept of artifacts [START_REF] Ricci | Give agents their artifacts: the A&A approach for engineering working environments in MAS[END_REF]. By following this multi-agent paradigm from the concepts to their implementation, MECSYCO ensures a modular, decentralized and distributable parallel co-simulation. MECSYCO implements the AA4MM concepts according to DEVS simulation protocol for coordinating the executions of the simulators and managing interactions between models. In the following, we describe these concepts and their specifications.

Operational Specifications

MECSYCO relies on four concepts to describe a multimodel. An m-agent A i (symbol in Figure 5b) manages a model m i and is in charge of interactions of this model with the other ones. The behavior of each m-agent corresponds to the DEVS conservative parallel abstract simulator which is based on the Chandy-Misra-Bryant (CMB) algorithm [START_REF] Chandy | Distributed simulation: A case study in design and verification of distributed programs[END_REF]4]. This algorithm is proven to be deadlock free and to respect the causality constraint [START_REF] Zeigler | Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems[END_REF].

Each interaction from an m-agent A i to an m-agent A j is reified by a coupling artifact C i j (symbol in Figure 5c). A coupling artifact C i j works like a mailbox: the artifact has a buffer of events where the m-agents can post their external output events and get their external input events. The coupling artifacts can transform the data exchanged between the models using operations that can be for instance, spatial and time scaling operations (converting kilometers to meters or hours to minutes), or aggregation/disaggregation operations [START_REF] Camus | Considering a multi-level model as a society of interacting models: Application to a collective motion example[END_REF]. Each m-agent A i sees its model m i as a DEVS atomic model thanks to its model artifact I i (symbol in Figure 5d). Therefore, I i acts as a DEVS wrapper for m i -i.e. it implements the DEVS simulation protocol functions for controlling m i evolution through s i . These functions, which are listed below, have to be defined for each simulation software:

• init() initializes the model m i . It sets the parameters and the initial state of the model, • processExternalEvent(e ini , t i , x k i ) processes the external input event e ini at simulation time t i in the k th input port of m i , x k i , • processInternalEvent(t i ) processes the internal event of the model m i scheduled at time t i , • getOutputEvent(y k i ) returns e k outi , the external output event at the k th output port of m i , y k i , • getN extInternalEventT ime() returns the time of the earliest scheduled internal event of the model m i .

The Figure 6 shows how these concepts are combined in order to perform the co-simulation of the barrel-filler factory. For each simulation software, we define a model artifact performing the wrapping with DEVS. Thanks to these artifacts the factory model can be simulated as the DEVS coupled model of Figure 4.

Defining the model artifacts for the two controllers is trivial as these models are already event-based. In previous works on MECSYCO like [START_REF] Vaubourg | Multi-agent multi-model simulation of smart grids in the MS4SG project[END_REF], the authors have created model artifacts for FMUs solely based on the FMI for co-simulation specifications. However as discussed in the following section, wrapping the two FMUs in DEVS in our more complex hybrid context requires defining a sound DEV&DESS model artifact.

MODEL ARTIFACT FOR HYBRID CO-SIMULATION OF FMUS

Foundation

As any model in MECSYCO, the FMU to integrate will be connected to the co-simulation by a model artifact. This artifact exposes a DEVS view of the FMU, and must allow it to deal with events. As stated in 3.1, to define such a model artifact we can rely on the DEV&DESS formalism as it can be embedded into DEVS, and as it offers a sound framework for describing hybrid systems.

As described by [START_REF] Zeigler | Embedding DEV&DESS in DEVS[END_REF], in its DEVS version a DEV&DESS model is composed of three components, each of them being formalized as a DEVS atomic model. With this structure, a DEV&DESS model can be incorporated into a larger DEVS schema as a coupled model. Thus the DEV&DESS model can be simulated using the DEVS simulation protocol. The three components composing the model are:

• A continuous component describing the evolution of the continuous part of the system according to continuous inputs, and producing continuous outputs. In our model artifact, we propose this component to correspond to the FMU we want to integrate into an hybrid co-simulation.

• An event-detection function determining when stateevents occur based on the continuous states of the model (i.e. the FMU state in our case).

• A discrete-event component describing the evolution of the discrete part of the system. In our model artifact, this component describes the behaviour of the FMU in the discrete-world, that is to say how it schedules internal events, how it produces and reacts to discrete inputs (i.e. external events), and what are the impacts of state-events. Potentially, for each of these events, the event-based component can change the whole DEV&DESS states, that is to say (1) its own state, (2) the continuous component state (thus creating a discontinuity in the FMU evolution) and

(3) the event detection function.

Application to FMU Components

For managing the continuous component evolution, the original DEVS version of DEV&DESS relies on a quantized integrator approach like the Quantized State Systems (QSS) method [START_REF] Kofman | Discrete event simulation of hybrid systems[END_REF]. This approach is based on state quantization instead of the time discretization used by traditional integration methods. QSS is well-suited for hybrid modeling as it makes the continuous component equivalent to a DEVS model which naturally integrates input events, and makes state-events detection trivial and costless. However, as stated before, we add in our model artifact an operational constraint: the continuous component corresponds to an FMU i.e. an equation-based model exported with its time-stepped solver as a black box onto which we have a limited control. By its time-stepped nature, an FMU can't be considered as a QSS model, and therefore we need to adapt the original DEVS version of DEV&DESS in our model artifact.

More precisely, an FMU component provides the following functionalities: (1) perform an integration for a given time-step (fmi2DoStep), and (2) set inputs and get outputs (fmi2SetReal/Integer/Boolean/String and fmi2GetReal/Integer/Boolean/String). We also assume that it is possible to implement a roll-back functionality to go one single integration step back. This last feature is feasible if the FMU component implements the fmi2GetFMUState and fmi2SetFMUState optional functions enabling to export/import the model state.

According to the FMI co-simulation specification, we consider that this FMU component produces outputs at a sequence of pre-define communication points. From our DEVS point of view, these communication points are seen as internal events producing external output events. In the same way, from our DEVS point of view we see updates of the continuous input values received by the FMU as input events.

The next section presents how we propose to implement the DEVS simulation protocol within our model artifact in order to respect the DEV&DESS semantic with these FMI constraints.

Functioning of the DEV&DESS Model Artifact for

FMU Components Getting the Time of the Next Internal Event

According to the DEVS semantic, the getN extInternalEventT ime() function must return the date of the earliest scheduled internal event in the model. In the DEV&DESS context, this date corresponds to the minimum between:

• the date of the next internal event scheduled in the discreteevent component, • the date of the next communication point of the FMU, • the date of the next state-event.

Getting the first two dates is trivial as they are a priori known. Things get more complex for the state-events: because of the numerical resolution of the equational model, state-events can only be detected after each integration step of the FMU, and their localization in time can only be approximated.

In order to get the date of the next state-event, we need to perform an exploration with the FMU to see if a state-event will occur before its next communication point. Thus, the component will always be "in the future" compared to the current simulation time. As according to the DEVS semantic the getN extInternalEventT ime() function must not change the state of the model, it is imperative to be able to come back to the previous state of the FMU which is the only legitimate state from the simulation point of view. The rollback capability of the FMU assures this feature as long as no new integration step is performed.

When a state event is detected during an exploration, we perform a bisectional search [START_REF] Mosterman | Hybrid dynamic systems: Modeling and execution[END_REF] in order to localize the stateevent as precisely as possible in the time. This search is formalized by the Algorithm 1 which, given the initial integration step ∆T and a number of iterations m (formalizing the search precision), positions the FMU as close as possible to the state-event occurrence. The algorithm basically progresses by a succession of integration steps whose duration δt is adapted according to state-event occurrences, and following a dichotomous strategy. As, again, the original state must always be accessible, and as only one integration step can be cancelled at a time, the algorithm always goes back to the legitimate state before performing a new integration step.

Algorithm 1 Bisectional search for state-event localization. According to the DEV&DESS semantics, when an event (internal, external or state-event) occurs at simulated time t, the equational component describes the continuous evolution of the system until t, and the event is processed by the discreteevent component. This behaviour is translated in our model artifact as follows.

INPUT: ∆T ∈ R + 0 , m ∈ N + 0 δt ← 0 ∆t ← ∆T
When the processExternalEvent(e ini , t, x k i ) function is called to report the occurrence of an external input event e ini into the x k i input port, the first step consists in rolling back the FMU to its previous state, which is, as stated in the previous section, the only legitimate state from the simulation point of view. Then the FMU performs an integration step until t in order to reach the point where the event occurs. Finally, if x k i is a continuous port, the FMU is parametrized accordingly. If x k i is a discrete port, the external transition function of the discrete-event component is triggered in order to process e ini .

In a similar way, when the processInternalEvent(t) function is called to process the next internal event, the FMU is rolled back to its previous state and an integration step is performed until t. If the next internal event corresponds to a communication point of the FMU, then the model artifact retrieves the continuous output ports values, and produces the external output events accordingly. On the other hand, if the next internal event corresponds to a state-event or the next internal event of the discrete-event component, then the internal transition function of this latter is called, which could produce external output events.

Known Limitation

A similar approach is used by DACCOSIM [START_REF] Galtier | FMI-based distributed multi-simulation with DACCOSIM[END_REF][START_REF] Camus | MECSYCO-DACCOSIM coupling[END_REF] to approach the date of a state-change, except DACCOSIM proceeds sequentially instead of bisectionally. A limitation of both solutions is that some state-changes might go undetected; for instance, if a boolean value changes twice during the exploration, the detection function will not see its value as modified. For this reason, it is important that the cosimulation designer carefully sets the date of the first data exchange between continuous and event-based domains so that only one state-change could take place within an exploration. Otherwise we could observe the occurrence of late propagation of internal events: let's assume the next communication point is set to t 10 and a boolean value changes at t 2 and t 9 . The first exploration, simulating from t 0 to t 10 will not detect the t 2 and t 9 events (because of the even number of statechanges). Let's imagine another agent propagates an event for t 8 . The equation-based component will roll back to t 0 and resume a simulation from t 0 to t 8 . The boolean value which changed at t 2 will be propagated with a time-stamped of t 8 instead of t 2 , which is the correct value.

IMPLEMENTATION AND USE-CASE EXECUTION

Model Artifacts Definition

In our use-case example, we define two DEV&DESS model artifacts I barrel and I tank to manage the integration of the barrel and tank FMUs into the discrete world. We define the discrete-event components and the event-detection functions of these model artifacts for wrapping these two models, .

In I barrel , the event detection function considers that a state event occurs when the level of water in the barrel FMU reaches the desired threshold (which is initialized at 1 liter). Thus, state-events correspond to switches of barrels.

The discrete-event component of I barrel has two discrete input ports named size and abort. Through the abort port, the component can receive requests for canceling the current barrel filling. When such an event is received at a date t, the component external transition function schedules an internal event at a date t + d -the internal event representing the switch of barrel, and d representing the reaction delay of the model. Through the size port, the component can receive update notifications of the desired level of water in the barrels. When such an event is received, the component external transition function stores the command in order to apply it at the next state event (i.e. after the current barrel is full) or next internal event (i.e. after receiving a cancel order).

When its internal transition function is triggered either by a state or an internal event, the discrete-event component represents the switch of barrel by: (1) producing through its barrel discrete output port an external event in order to signal the barrel departure, (2) resetting the FMU state (thus setting the water level back to 0) in order to represent the arrival of a new barrel, and (3) changing the threshold of the event detection function if a command awaits application.

In I tank , there is no state-event, so the event-detection function is disabled. The discrete-event component does not have any output port, but has one input port in order to receive command to open or close the water inlet. When the command is received, the event-driven component changes the value of the valve variable in the FMU accordingly.

Implementation

We used the Java version of MECSYCO (available at http://mecsyco.com) in order to implement our DEV&DESS model artifacts. This version of MECSYCO relies on the OMG standard Data Distribution Service (DSS). The eventbased models were directly implemented in Java. The equational models were written in Modelica language and exported in FMI 2.0 using the Dymola software. Our DEV&DESS model artifact relies on JavaFMI [START_REF] Hernández-Cabrera | [END_REF] in order to interact with the FMUs. Yet let's emphasize that FMUs were only used as illustrative examples. The same results can also be achieved (and indeed were) with continuous models written directly in Java, provided that a wrapper code is developed to offer an FMU-like interface for the Java model.

Results

The Figure 7 shows the results of the MECSYCO barrelfiller factory co-simulation (with the reaction delay of I barrel equals to 0.01). At t = 0, the tank contains 7 l and the barrel is empty. At t = 0.5, the valve opens and the liquid starts flowing from the tank into the barrel (volume of liquid in the tank continuously decreases while volume in the barrel increases). At t = 1.016, the volume of liquid in the barrel reaches 1 l. This triggers the emission of the barrel and a new barrel is set up (volume in barrel is 0 again). At t = 1.613 the 2 nd barrel is full (1 l). Again, that triggers the emission of the barrel and a new barrel is set up under the tank. But at t = 1.9 the factory is ordered to abort the current barrel. After a very small delay, at t = 1.91, the 3 rd barrel, containing only 0.43 l, is pushed out and a new barrel is set up and starts filling up. At t = 2.715 an event notifying that this 4 th barrel is full is generated and a 5 th barrel is set up. But at t = 3.2 the valve is closed. The tank stops emptying and the volume in the barrel stays the same. At t = 5.2 the valve opens again and the 5 th barrel resumes its filling. At t = 5.773 this 5 th barrel is pushed out and a 6 th barrel is installed. But at t = 6.5, before this 6 th barrel reaches 1 l, the desired volume in the barrel is changed from 1 l to 0.5 l. The factory keeps filling up to 1 l the 6 th barrel but when that old threshold is reached at t = 7.342, the new target volume is taken into account for the filling of the 7 th barrel: at t = 8.535, when the volume in the 7 th barrel reaches 0.5 l, the barrel is pushed out and replaced by a new one. As the volume in the tank is getting low, the output rate of the tank decreases and it takes a little longer for this 8 th barrel to fill up and be replaced by a 9 th barrel which reaches 0.5 l at t = 15.139. The 10 th barrel, installed at t = 15.139, fills up to 0.07 l but afterwards the tank is empty.

The Table 1 compares the times where the barrels are generated with our solution (with m = 100), and with a classic FMU co-simulation strategy (still performed with MECSYCO but without using our DEV&DESS model artifact) where the events are detected and integrated at each communication points only. For each solution, we test different communication step sizes for the numerical resolution of the FMU. We can see that with a classic FMU co-simulation strategy, events occurrences are directly dependent on the communication step size. On the opposite, with our solution events occur at the same simulation times (with a precision of 10 -3 at least) no matter the configuration required by the FMU numerical resolution. Thus, our solution enables to reconcile both the event-based and the equational worlds needs.

RELATED WORK

Aside from the papers already cited in the previous sections, other works related to hybrid modeling should be mentioned here. In [START_REF] Muller | Linking FMI-based components with discrete event systems[END_REF], the authors integrate FMUs into Ptolemy II event-based models by relying on a similar exploration mechanism for detecting state-events. However, this solution does not provide the same richness of expression offered by our DEV&DESS wrapper: events can't change the eventdetection function, and discrete behavior like internal events scheduling can't be specified.

The Heterogeneous Flow System Specification (HFSS) [1] also offers an interesting hybrid M&S framework as it brings numerical multi-rate integration methods for modeling and simulating continuous parts of the systems. However, this formalism is not yet fully integrated in DEVS [START_REF] Zeigler | Embedding DEV&DESS in DEVS[END_REF], and therefore doesn't benefit from the strong integrative power of this latter. Yet, defining an HFSS wrapper for FMU-like components should be investigated in future works.

PERSPECTIVES AND CONCLUSIONS

In this article, we proposed a fully implemented and functional wrapper (called model artifact in the MECSYCO paradigm) for integrating FMU 2.0 components into a hybrid co-simulation. This wrapper implements the DEVS simulation protocol based on the DEV&DESS semantics and the FMI 2.0 operational constraints. Thanks to our wrapper, FMU and event-based components can interact within the rigorous integrative framework of DEVS. The hybrid cosimulations of these components can be then managed by one of the many DEVS simulation algorithms, in our case the parallel conservative one. Thanks to the strong foundations of DEV&DESS, this wrapper is generic: there is no need to change the algorithms when the model is changed. Yet our solution is evolutionary: one can still keep the framework and change the algorithms, for instance the event localization one.

Our solution will be used in smart spaces and large smartgrid simulations which will provide testbeds richer than our use case (e.g. more models, larger models, distributed components) and drive future evolutions. In future works, we plan to test other state-event localization strategies such as the Illinois algorithm [START_REF] Moler | Are we there yet? Zero crossing and event handling for differential equations[END_REF] or a combination of existing algorithms. Having different strategies available would enable adapting our solution to different operational constraints, such as the simulation performance (e.g. where we should limit the number of rollbacks of a large FMU), or the simulation accuracy. We also want to integrate in our wrapper the new eventdetection features planned for the FMI 2.1 standard as soon as they will be available. Finally, in order to manage a set of FMUs instead of a single one, we also plan to integrate DACCOSIM [START_REF] Galtier | FMI-based distributed multi-simulation with DACCOSIM[END_REF] as a continuous component into our model artifact. This integration can be done directly through the DACCOSIM interface, or by embedding DACCOSIM into an FMU (using for instance the FMU builder of JavaFMI). 1. Comparison of the barrels output times (rounded to 10 -3 ) between our DEV&DESS integration of the FMU (Series1) and a classic FMU co-simulation strategy (Series2).

Figure 1 .

 1 Figure 1. The barrel-filler factory.

Figure 2 .

 2 Figure 2. The tank model viewed in Dymola.

Figure 3 .

 3 Figure 3. The barrel model viewed in Dymola.

Figure 4 .

 4 Figure 4. DEVS view of the barrel-filler factory.

Figure 5 .

 5 Figure 5. Symbols of the MECSYCO components.

Figure 6 .

 6 Figure 6. MECSYCO architecture for the barrel-filler factory.

Figure 7 .

 7 Figure 7. Simulation results.

  ADDITIONAL AUTHORSstep size t barrel1 t barrel2 t barrel3 t barrel4 t barrel5 t barrel6 t barrel7 t barrel8 t barrel9

	Series1	0.001 0.01 0.1	1.016 1.016 1.016	1.613 1.613 1.613	1.910 1.910 1.910	2.715 2.715 2.715	5.773 5.773 5.773	7.342 7.342 7.342	8.535 8.535 8.535	10.412 15.139 10.412 15.139 10.412 15.139
	Series2	0.001 0.01 0.1	1.017 1.020 1.100	1.615 1.620 1.800	1.910 1.900 1.800	2.716 2.710 2.600	5.774 5.770 5.700	7.344 7.340 7.300	8.538 8.540 8.500	10.419 15.167 10.430 15.230 10.400 15.300
	Table


Daniel Laqua

BELGIAN INTERNATIONALISTS, THE GREAT WAR AND THE QUEST FOR PEACE

In 1932, Henri Pirenne -widely renowned for his work on medieval towns -published the final part of his Histoire de Belgique. The first instalment of his magnum opus had appeared more than three decades earlier and tackled a period long before Belgium's independent statehood, from Antiquity to end of the High Middle Ages 2 . It was only with volume VII that Pirenne finally reached the era since the Belgian Revolution of 1830. The account drew a wider picture of the country before the First World War. In this context, Pirenne argued that Belgian civilisation was « international at its base » as it was « merely the combination of the influences to which the country is exposed at the sensible spot of Europe that it occupies » 3 . With such comments, Pirenne helped to nourish national narratives that cast Belgium as an international meeting ground or « crossroads of Europe » 4 .

Evidently, such discourse needs to be approached with caution: after all, ideas of nationhood tend to be based on claims of distinctness. What Pirenne and others seemed to describe as a Belgian speciality -namely receptiveness to external influences -could equally be claimed by many nations. Nonetheless, the assertions about Belgium's international links were more than mere rhetoric. In the Belle Époque, the country was one of the major sites for international congresses. Some of these events coincided with world's fairs that were hosted on Belgian soil. Indeed, Belgians were among the most prolific organisers of world exhibitions. In the three decades between 1885 and 1914, the country staged six such events -not just in Brussels (1897 and 1910), but also in Antwerp

Linked to its proclivity for hosting international gatherings, Belgium became the base for various kinds of international organisations. One such type included scholarly institutions with an explicitly international remit, exemplified by the Institute of International Law in Ghent (1873) and by the Brussels-based Solvay institutes that were established between 1902 and 1913 6 . Furthermore, the Belgian government managed to attract intergovernmental bodies such as the International Maritime Committee (1895) and the Sugar Union (1902), forming part of a foreign-policy agenda that embraced internationalism 7 . Meanwhile, political activists used meetings in Belgium to consolidate their transnational ties, for instance via the International Freethought Federation (1880) and the International Socialist Bureau (1900) 8 . Alongside such institutional processes, there were further dimensions to the country's role as site for international encounters: in the cultural realm, Belgian authors and artists engaged with vibrant cultural movements such as Symbolism and Art Nouveau ; in religious terms, Belgium became a « laboratory » in which the Catholic Church tested its response to the culture and politics of modernity 9 .

The case of Belgium thus illustrates the extent to which the decades before the First World War were an age of internationalism -a period in which activists and intellectual fostered transnational cooperation in manifold ways 10 . Yet, as Pirenne acknowledged, internationalism coexisted with nationalism. In his Histoire de Belgique, he described the two phenomena as « contradictory tendencies that characterised the European civilisation of the era » 11 . Such comments should not lead us into thinking that the forces were diametrically opposed: instead, they frequently intersected. The present essay examines this relationship. In doing so, it addresses one major question: how did groups and individuals act internationally at a time of intense nationalism? To this end, the piece considers the ways in which protagonists of internationalism responded to the First World War. Four years of military conflict resulted in death and destruction on an unprecedented scale and the rupturing of many 6 On the Institute of International Law, see M. KOSKENNIEMI transnational ties. However, it also gave rise to campaigns and projects for a new international order -a quest which the historian William Mulligan has called The Great War for Peace. Mulligan has viewed peace as being « at the centre of the First World War, providing meaning to the conflict » while noting the « enduring legacy » of visions of peace that had been articulated in this period [START_REF] Mulligan | The Great War for Peace[END_REF] . A focus on this aspect can highlight the setbacks and possibilities of internationalism under challenging circumstances.

Three Belgians Internationalists

Rather than examining ideological or institutional transformations, the present essay focuses on three individuals whose activism illustrates the tribulations and transformations of internationalism. The choice of examples allows us to consider different movements: we will first consider a pacifist, secondly a key figure of international socialism and, finally, a female campaigner whose efforts shed light on different features of women's activism.

The pacifist in question is Henri La Fontaine (1854-1943), who represented the Belgian Workers' Party (Parti Ouvrier Belge) in the Belgian Senate from 1895 onwards. La Fontaine was involved in a wide range of international projects, many of which were collaborative ventures with the bibliographer Paul Otlet [START_REF] Rayward | The Universe of Information: The Work of Paul Otlet for Documentation and International Organisation[END_REF] . One example was their joint foundation of the Union of International Associations (1910) -a body that aspired to coordinating the efforts of all kinds of international organisations. Later on, this impetus to centralise international efforts was reflected in their campaign for a Cité Mondiale, a world capital city for which they regarded Belgium as an ideal site [START_REF] Van Acker | A Tale of Two World Capitals: The Internationalisms of Pieter Eijkman and Paul Otlet[END_REF] . La Fontaine's greatest renown, however, derived from his involvement in the peace movement. Having co-founded the Belgian Arbitration and Peace Society (Société Belge de l'Arbitrage et de la Paix) in 1889, he became a key figure in the meetings and organisational structures of international pacifism. From 1907, he chaired the International Peace Bureau, which brought together the representatives of different national peace societies and held near-annual Universal Peace Congresses. In 1913, La Fontaine's efforts were rewarded with a Nobel Peace Prize, with the secretary of the awarding committee praising him as « the true leader of the popular peace movement in Europe » [START_REF] Moe In | Nobel Lectures in Peace[END_REF] .

The second figure under consideration is the socialist Camille Huysmans (1871-1968). In national terms, he is mainly known for two reasons: during the interwar years, Huysmans was a leading figure in promoting Flemish cultural interests within the Belgian state and became Mayor of Antwerp in 1933. In tackling the country's language question, the socialist Huysmans worked across party lines, notably with the liberal Louis Franck and the Catholic Frans Van Cauwelaert. At the same time, he also cooperated with protagonists of the Walloon Movement, drafting the Compromis des Belges with Jules Destrée in 1929 [START_REF] Destrée | The 'Compromis des Belges[END_REF] . The second reason why Huysmans's name features in national history books is that in July 1946, he became prime minister -albeit only for seven months [START_REF] Conway | The Sorrows of Belgium: Liberation and Political Reconstruction, 1944-1947[END_REF] . His inclusion in the present essay, however, is attributable to another aspect of his life: not his domestic role, but his involvement in international socialism. In 1900, socialist parties from across Europe and North America had established the International Socialist Bureau to coordinate the efforts of the Second International, which had formed eleven years earlier. Based in Brussels, the new body was chaired by Emile Vandervelde, leader of the Belgian Workers' Party. As Vandervelde's biographer Janet Polasky has put it, Vandervelde « nurtured the comradeship that held the [international socialist] movement together until the war and defined the democratic socialist strategy that endured the war » [START_REF] Polasky | The Democratic Socialism of Emile Vandervelde: Between Reform and Revolution[END_REF] . In 1905, Huysmans joined the Brussels-based body as its secretary; his involvement meant that « the Bureau and its executive committee began to operate more smoothly » 19 . Over the subsequent years, Huymans maintained a correspondence with socialist leaders from different countries and helped to organise the movement's international congresses.

The third activist is Eugénie Hamer -a female pacifist whose biographical details are somewhat sketchy [START_REF] Gubin | Eugénie Hamer[END_REF] . Hamer's trajectory differs from the careers of La Fontaine and Huysmans in that she did not become the leader of a major international association or ascend to high political office. Born in Leuven/Louvain in 1865, much of her pre-war activism occurred within middle-class circles in Antwerp. Her public engagement encompassed different facets of Belgian women's activism, as exemplified by her involvement in the Women's Circle of the Red Cross (Cercle des Dames de la Croix Rouge) 21 . For the purposes of our discussion, it is her role in the Belgian Alliance for Peace through Education (Alliance Belge pour la Paix par l'Éducation, ABPE) that is most significant. Having been founded in 1906, the ABPE counted around 1,000 members by 1914 [START_REF] Lubelski-Bernard | Les mouvements et les idéologies pacifistes en Belgique 1830-1914[END_REF] . It presented itself as apolitical and was not feminist as such, but it maintained connections to the worlds of feminism. As the historian Julie Carlier has put it, the ABPE was « firmly embedded in the same social reformist circles in which feminists moved »23 .

The ABPE's focus resonated with a strand of pre-1914 pacifism that treated education as the foundation for a peaceful future24 . Hamer herself was a proponent of this view: at the First National Peace Congress of Belgium in 1913, she presented a report on « pacifist propaganda » and stressed the importance of educational efforts in this context [START_REF][END_REF] . Such arguments could be cast in feminine terms: after all, education was a domain in which women had a public role even in places where they lacked political rights. Educational questions thus provided opportunities to speak up on matters of international politics [START_REF]A later example is the way in which female educators engaged with the League of Nations in the 1920s and 1930s[END_REF] . The theme of a female contribution to peace could have further political implications. For instance, according to Eliane Gubin, Antwerp activists associated with the ABPE portrayed women's suffrage as a potential safeguard against future wars [START_REF] Gubin | Du politique au politique : parcours du féminisme belge (1830-1914)[END_REF] . Seen from this angle, Hamer's activism draws attention to the interplay between women's activism, pacifism and feminism. While Hamer's pre-1914 work mostly occurred in the national arena, it was also a form of internationalism. After all, the ABPE pursued the quest for closer international cooperation and was part of the Alliance Universelle des Femmes pour la Paix par l'Éducation. In 1910, Hamer represented the ABPE at the Universal Peace Congress held in Stockholm [START_REF]See the fleeting reference to an account written by Hamer in « Variétés : Revue des Revues[END_REF] .

La Fontaine, Huysmans and Hamer differed from one another in terms of their cultural background: La Fontaine was a French-speaker from Brussels and Huysmans a Dutch-speaker from Antwerp. Hamer was Francophone, living in a Dutch-speaking city where French was widespread among the élite [START_REF] Carlier Notes | the ABPE[END_REF] . Even beyond the question of language, the three represented somewhat different milieus. Although both La Fontaine and Huysmans were members of the Belgian Workers' Party, the former exemplified a segment of Belgian socialism that had much in common with the liberals: like many of them, he had trained as a lawyer and, throughout his career, prioritised reform over revolution. The third figure -Hamer -was not associated with socialism. Indeed, in the interwar years, she wrote for a Catholic newspaper, La Métropole30 .

Notwithstanding such differences, La Fontaine, Huysmans and Hamer shared various experiences and interests. Their commitment to social reform meant that the spheres of their engagement overlapped. Most significantly, all three drew on contacts that cut across national boundaries: the transnational bonds of pacifism, socialism and women's activism. Having introduced La Fontaine, Huysmans and Hamer, we shall now consider what their wartime experience can tell us about the fate of internationalism in a time of conflict.

Henri La Fontaine: The Peace Movement and the Great War

Henri La Fontaine was a widely respected peace leader who moved within international environments with great ease. As a leading historian of Belgian pacifism noted, he « dedicated his whole life » to forging closer connections between people from different nations31 . However, the German attack on Belgium demonstrated his national attachments. In light of the Belgian experience of invasion and occupation, La Fontaine initially rejected calls to convene a session of the International Peace Bureau. When such a meeting was eventually held in January 1915, he asserted his Belgian identity, asking the German delegates to denounce their government's act of aggression 32 . The prospects for gaining a satisfactory response were limited during the war: some Germans had swung behind their government, while more critical wartime voices faced censorship and surveillance 33 . In this respect, La Fontaine's stance reflected wider ruptures within the international peace movement. Indeed, it took until 1921 before a Universal Peace Congress took place with German involvement.

At the same time, the war generated new international commitments and experiences. In 1915, La Fontaine moved to the USA, where he stayed until the end of the war. This was hardly his first American encounter: for instance, in 1904 he had attended the Universal Peace Congress in Boston. Furthermore, between 1910 and 1914, some of his activities received financial backing from the Carnegie Endowment for International Peace. Compared to these earlier encounters, La Fontaine's wartime stint in the USA resulted in a more sustained engagement with American audiences and debates. In this respect, his experience reflected a wider transatlantic development. Long before the USA's entry into the war, « poor little Belgium » met with sympathy among members of the American public. The creation of the American Committee for the Relief of Belgium was a striking reflection of this development [START_REF] Barnett | Empire of Humanity: A History of Humanitarianism[END_REF] . Furthermore, as Michaël Amara has shown, the USA were a target for Belgian propaganda efforts that -either explicitly or implicitly -made the case for American support or intervention [START_REF] Amara | La propagande belge et l'image de la Belgique aux États-Unis pendant la Première Guerre Mondiale[END_REF] . La Fontaine's role during the war certainly fitted into this category, as he conveyed his country's plight to American audiences. He continued to draw attention to Belgian matters after the USA had joined the war effort [START_REF]Plea for Belgian Soldiers: Men in Trenches Need Comforts, Says Senator La Fontaine[END_REF] . La Fontaine's concern for the fate of his country became evident as late as May 1918, when he looked ahead to an end of conflict and contemplated the nature of post-war peacemaking. He suggested that Belgium would have to be the place where diplomats would meet. This location was meant to drive home to the Central Powers the damage that they had done:

They have to come, the representatives of the outlaw nations, as to a new and more impressive Canossa, to the land they have crushed, impoverished, spoiled, robbed, slandered, crucifiedthe land which will remain the symbol of their wickedness, but also the symbol of what right means to a world reborn and enlightened [START_REF] Fontaine | The Land Where Peace Is to Be Made[END_REF] .

It would, however, be wrong to view La Fontaine's wartime stance as a purely national one. Indeed, he continued to affirm his belief in international cooperation. Even before moving to the USA -and still fresh under the impression of the German invasion -he argued that a peaceful future should not only involve a « remodelling » of European law, but had to extend to the cultural realm. As he put it, « [f]rom our national songs, also, the words of hate and ill-will should disappear» [START_REF] Fontaine | A Pacifist View[END_REF] . Indeed, the most prominent strand of La Fontaine's wartime activism involved ideas about peace and cooperation. Based on his existing profile as a peace leader and Senator, he could present his views alongside other prominent figures. For instance, in May 1915 he spoke at the Lake Mohonk Conference on International Arbitration, whose participants included the US Secretary of War, Lindley Miller Garrison, and in November 1916 he shared a platform with former US Secretary of State William Jennings Bryan [START_REF]Peace Men Praise President's Course[END_REF] . In the last two war years, La Fontaine also had a lecturing stint at the City College of New York, where he taught « the causes of war », « aspects of the world organization of nations » and « the philosophy of international relations » [START_REF]Courses of Lectures by La Fontaine[END_REF] .

The war did not only result in speaker engagements for La Fontaine, but also inspired him to draw up concrete plans for the future world order. In 1916, he presented his scheme for a Magnissima Charta 41 . The scheme was published under the auspices of the World Peace Foundation. The latter organisation had originated in a School of Peace founded by the American philanthropist Edwin Ginn [START_REF] Rotberg | A Leadership for Peace: How Edwin Ginn Tried to Change the World[END_REF] . La Fontaine's publication appeared at a time when many American internationalists also discussed plans for a future world organisation [START_REF] Th | To End All Wars: Woodrow Wilson and the Quest for a New World Order[END_REF] . In his preface to this text -signed on the American Independence Day of 1915 -La Fontaine referenced his transatlantic journey while appealing to the political traditions of his host country. He argued that the text had been [b]orn in distress and exile, in the midst of the people who, seven centuries ago, was the first to draft for the benefit of mankind a pact of liberty, written on the open sea, the brotherly highway between the peoples, swung by the waves which no human power can ever enslave or subdue, -completed on the soil of the most cosmopolitan democracy, where government of the people, by the people and for the people is a living reality [START_REF] Fontaine | The Greatest Solution[END_REF] .

According to the Belgian pacifist, the principles that ensured domestic order equally applied to questions of global order. In other words, just as individual states needed laws, so did the « society of states ». The title of his publication emphasised this line of argument through its allusion to Magna Carta 45 . In terms of institutional arrangements, La Fontaine proposed a regular conference of states, which would maintain its own commissions and create new international conventions 46 . To ensure the coordination of these activities, La Fontaine envisaged an International Administrative Council and a Permanent International Secretariat 47 . Nonetheless, there were clear limitations to the new world organisation as he conceived it. While La Fontaine favoured the creation of an international fleet, he stopped short of proposing a body that might impose military sanctions on those who violated international law: he described talk « of police force, of international police force» as « truly somewhat venturesome ». [START_REF]For La Fontaine's proposals regarding an international fleet[END_REF] Instead, La Fontaine preferred « indirect means of constraints » -namely measures in terms of diplomacy, finance or communications, to be ordered by an International Court of Justice 49 . In these respects, La Fontaine's text illustrates the competing visions regarding the nature of a future League of Nations, in particular with regard to its potential sanctioning mechanisms [START_REF] On | The League That Wasn't: American Designs for a Legalist-Sanctionist League of Nations and the Intellectual Origins of International Organization, 1914-1920[END_REF] .

Many of La Fontaine's ideas seem to resonate with the tenets that we associate with Wilsonian internationalism. This goes for the idea of a world organisation, but also for the emphasis on national self-determination and democracy. At the same time, in focusing on international law, La Fontaine revealed his ongoing adherence to a major trope of pre-war pacifism [START_REF] Guieu | For an overview of the currents that La Fontaine engaged with[END_REF] . Indeed, as a step towards a new world order, he proposed a meeting that would continue the work of the Hague Peace Conferences of 1899 and 1907. Such views suggest that La Fontaine did not regard the war itself as a defeat for the principles of the peace movement: the conflict merely seemed to prove that governments had not sufficiently listened to its demands.

Camille Huysmans: The Socialist Dilemma

Similar to the rifts within the peace movement, international socialism underwent major divisions during the war. As late as 29 July 1914, socialists from different countries gathered in Brussels at the Cirque Royal to denounce their governments' war policies. However, shortly afterwards, many socialists rallied around their national cause. As a result, it was mostly minority groups within the respective parties that sought to continue to work across enemy lines. The most radical critics formed the Zimmerwald Left, with the likes of Lenin denouncing others as « social chauvinists » [START_REF] Nation | War on War: Lenin, the Zimmerwald Left and the Origins of Communist Internationalism[END_REF] .

Camille Huysmans formed part of neither of these camps: while rejecting the stance of the Zimmerwald Left, he nonetheless worked across enemy lines. As a step towards this aim, he moved the International Socialist Bureau to the neutral Netherlands. Furthermore, Huysmans submitted peace proposals to separate meetings planned by the socialist parties of the neutral countries (Copenhagen, January 1915), of the Entente (London, February 1915) and of the Central Powers (Vienna, April 1915) [START_REF]Democratic Socialism of Emile Vandervelde[END_REF] . This willingness to reach out attracted criticism among his Belgian comrades. Huysmans himself expressed his unhappiness about the « sniping » that he encountered from Allied socialists 54 . Yet, he expressed no regrets: It is not necessary to say, also, that to a Belgian it was not always very pleasant to find himself [sic] with Social-Democrats who had approved the credits which had served to put his country to fire and sword. But I considered it to be my duty not to write a word which would have wounded one of the affiliated parties [START_REF]An Address by Camille Huysmans[END_REF] .

Such statements indicate the difficulty of reconciling international commitments with national concerns. Huysmans did not downplay the injustices carried out by the Germans. He stated that « [n]othing excuses their cruelty; they are covered with shame » [START_REF][END_REF] . Nonetheless, he championed transnational dialogue instead of operating on a purely national basis. His stance contrasted with that of Emile Vandervelde, who had taken up a post in the Belgian government after the outbreak of war. Janet Polasky, however, suggests that it would be misleading to view the two as complete opposites: « Vandervelde not only tolerated Huysmans's leadership of the International throughout the war, he seems to have been glad that Huysmans was doing what he was doing » [START_REF] Polasky | Democratic Socialism of Emile Vandervelde[END_REF] .

Huysmans contradicted the notion that the war had seen the collapse of socialist internationalism. In a newspaper interview of March 1916, he claimed that « The war has no more destroyed the International Socialist organisation than it has caused the Catholic Church to disappear » [START_REF] Huysmans | The Politics of the International[END_REF] . This comment echoed a point he had raised two months earlier: « Has the Catholic Church ceased to live because some German Catholic soldiers found themselves face to face with Catholic Belgian soldiers, on the two banks of the Yser? » 59 . With such arguments, Huysmans acknowledged the existing conflicts while affirming that they did not diminish the internationalist principles underpinning any form of socialism.

Arguably the most striking effort to defend socialist internationalism occurred in 1917, when Huysmans was the secretary of the projected Stockholm Conference [START_REF] Geldolf | [END_REF] . This peace initiative was prepared by a Dutch-Scandinavian Committee, involving the Dutch socialist Pieter Troelstra and the Swedish social democrat Hjalmar Branting. Over several months, socialist leaders from neutral and enemy nations travelled to the Swedish capital to prepare the conference, including such prominent figures as Friedrich Ebert from Germany and Victor Adler from Austria. Yet, David Kirby has concluded that the venture « was doomed from the start by the inability of the socialist parties of the belligerent countries to return to the principles of internationalism enunciated by the Second International before 1914 » [START_REF] Kirby | International Socialism and the Question of Peace: The Stockholm Conference of 1917[END_REF] .

Indeed, by August 1917, the initiative had effectively collapsed, owing to three major factors: firstly, national governments in many cases created obstacles for participation in the event. For the British Labour politician Arthur Henderson, support for the Stockholm preparations even resulted in his resignation from Lloyd George's cabinet [START_REF] Winter | Socialism and the Challenge of War: Ideas and Politics in Britain 1912-1918[END_REF] . The second reason was the Bolsheviks' promotion of an alternative event -and socialists in other countries were divided as to how respond to this [START_REF] Vandervelde Even | spoke of three competing plans for a conference: apart from the Dutch-Scandinavian initiative[END_REF] . Indeed, Huysmans himself expressed his scepticism about the Bolshevik stance. A few months later, he commented on the October Revolution and argued that it would not bring about a democratic peace. He described Russia as being « under a new czarist regime which socialists have been invited to admire and which they find impossible to even consider » [START_REF]Hope of 'People's Peace' Killed by Bolsheviki, Says Belgian Socialist Leader[END_REF] . The third explanation for the collapse of the Stockholm initiative was that many Allied socialists were too concerned about meeting their former comrades from the Central Powers. This stance extended to Huysmans's own party. G. D. H. Cole argued that « the expatriated Belgians indeed became the most intransigent element in the International, taking a strong stand against meeting the German socialists as long as the war continued» [START_REF] Cole | Communism and Social Democracy 1914-1931[END_REF] .

Among Belgian socialists, reservations about transnational cooperation continued during and beyond 1918. In August 1918, Emile Vandervelde and Louis de Brouckère rejected an offer to participate in an international conference, claiming that « the declarations, and still less the acts of the German Majority Socialists » did not met the conditions for such a meeting [START_REF] Vandervelde | [END_REF] . In February 1919, the Belgian Workers' Party remained unrepresented at the first major post-war meeting of socialists, the Bern Conference. In this respect, Huysmans proved to be a somewhat exceptional case. He has been described as being « firmly committed to the cause of the Entente » [START_REF] Kirby | International Socialism and the Question of Peace[END_REF] , yet his activism illustrates the ambiguities of international socialism during wartime. as well as neutral nations. The American social reformer Jane Addams later stressed its importance: « During a year when the spirit of internationalism had apparently broken down, they came together to declare the validity of internationalism which surrounds and completes national life. » [START_REF] Addams | Women and Internationalism[END_REF] Addams herself chaired the proceedings. She had travelled to Europe with other members of the Women's Peace Party, an organisation that American feminists had founded in January 1915 « to demand that war be abolished » [START_REF]Women's Peace Party: Preamble and Platform adopted at Washington[END_REF] . In order to attract support from different camps, the congress organisers concentrated on two principles, namely « the pacific settlement of international disputes and the extension of suffrage to women » [START_REF] Patterson | The Search for Negotiated Peace: Women's Activism and Citizen Diplomacy in World War I[END_REF] . Yet, the very act of convening with activists from the invader nation meant that Belgian participants risked accusations of insufficient patriotism.

What, then, about the Belgian delegation? As late as February 1915, Jacobs had mentioned the difficulty of attracting Belgian supporters [START_REF] Wilmers | Pazifismus in der internationalen Frauenbewegung 1914 -1920: Handlungspielräume, politische Konzeptionen und gesellschaftliche Auseinandersetzungen[END_REF] . Leading Belgian feminists either declined the Dutch invitation or left it unanswered. Léonie La Fontaine -a key activist and Henri La Fontaine's sister -expressed her sympathy and explained her absence with reference to her ill health. Yet, as Annika Wilmers has noted, her stance was « not free from contradictions »: while speaking of dialogue, she also adopted a « very patriotic and highly Germanophobic attitude » 78 . As a result, the Belgian presence at The Hague only amounted to five women. Hamer represented the ABPE alongside another Belgian delegate, Marguerite Sarten. The sole other Belgian organisation that was listed was a Cercle de Dames et Jeunes Filles Sionistes from Antwerp. Owing to their complicated journey from occupied Belgium, the Belgian participants only arrived after the start of the conference, making a celebrated entry. Following a German proposal, all five Belgians were seated at the platform [START_REF] Balch | Journey and Impressions[END_REF] . In this respect, their case suggests the potential for dialogue at a time of hostility. In looking back, the American delegate Emily Balch argued that there had been « not one clash or even danger of clash over national differences», claiming that all participants had shared « the same moving consciousness of the development of a new spirit which is growing in the midst of war as the roots of the wheat grow under the drifts and tempests of the winter». 80 Balch's assessment can partly be explained by the desire to convey an optimistic message to domestic audiences. Closer scrutiny of the events at The Hague reveals that the plight of Belgium clearly affected the proceedings. Although, as chair, Addams rejected the proposal of a specific debate on Belgian matters, Annika Wilmers has argued that « [m]any congress resolutions… can be understood as a reaction to the situation of Belgium » [START_REF] Wilmers | [END_REF] . At the same time, she has noted the « tense relations between the Belgians and the other participants » 82 .

In their quest to avoid controversy, the congress organisers excluded questions such as war guilt from the discussions [START_REF]Quelques détails sur le congrès : Conditions des débats[END_REF] . By contrast, the Belgian delegates sought recognition for the situation that their country was in. At various points, they protested against statements which, they felt, insufficiently acknowledged their country's condition. For instance, Hamer proclaimed that she was unable to sign up to a general call for peace, as she was « Belgian before everything else » 84 . Her language bore similarities to the stance of Henri La Fontaine who, at the 1915 meeting of the International Peace Bureau, had stated that « As much as I am… an internationalist, I am also… Belgian » 85 . Yet, it is worth noting that Belgian contributions at The Hague could also be cast in more positive terms. The French socialist Jean Longuet claimed that Hamer had spoken « in moving terms » about the need for a peace based on justice. He further mentioned a speech by Bala Birnbaum of the Jewish women's group from Antwerp. As he put it, her contribution stood for all those who had suffered persecution. Birnbaum ended her remarks with the slogan « Vive la Belgique! » -a point at which, according to Longuet, emotion swept through the « systematically neutralist assembly » like « an electric current », with the applause even extending to the German delegation [START_REF] Bigot | Le Congrès de La Haye[END_REF] . Such statements illustrate how differently the debates at The Hague could be framed.

Notwithstanding various points of conflict, the Hague congress agreed on resolutions that ranged from a general protest against war to the insistence that any territorial transfer be conditional on the consent of the affected population 87 . Delegates also demanded women's suffrage, describing « the combined influence of women of all countries » as « one of the strongest forces for the prevention of war ». As for the future order of Europe, the participants suggested that a « federation or a council of European powers should not be considered impossible from the very experience of the nations now at war » [START_REF] Addams | Women and Internationalism[END_REF] . In calling for a « Permanent Belgian branch [START_REF] Laqua | The Age of Internationalism[END_REF] . Hamer herself also engaged in new internationalist ventures after the war, seeking to reconstitute the ABPE as well as fostering Belgo-Polish links [START_REF] Gubin | Eugénie Hamer[END_REF] .

Conclusions

What do the cases of La Fontaine, Huysmans and Hamer tell us? Their trajectories certainly shed light on the extent to which internationalism had been a lively and multifaceted phenomenon before the war. All three figures were involved in causes that were construed as international in scale, and all three engaged in transnational cooperation to advance their objectives. After the unprovoked aggression on Belgium, they were confronted with a situation whereby their own country had become an international cause in itself. The examples that have been discussed highlight the extent to which the war affected existing transnational bonds.

In this respect, the story seems to be a rather bleak one. Yet, it is not always advisable to view events through the prism of conflict versus cooperation. Each of the three cases provides us with examples of how internationalism survived under difficult circumstances. Furthermore, all three cases in some respects pointed towards the future. For instance, the congress at The Hague ultimately laid the groundwork for WILPF, one of the leading pacifist organisations of the interwar years. Although Huysmans's wartime initiative for a peace conference failed, he continued to make plans for the time ahead, for instance by contributing to the International Affairs Advisory Committee of the British Labour Party [START_REF] Winter | La Fontaine in the context of intellectual cooperation during the interwar years[END_REF] . Finally, La Fontaine's wartime writings formed part of wider discussions on the shape of a future League of Nations. His own engagement with such question was far from purely theoretical: he was an advisor to the Belgian delegation at the Paris Peace Conference, remained a tireless presence within the interwar peace movement and lobbied for the creation of an intellectual wing of the League -in a way the antecedent of UNESCO 100 . Seen from this angle, the Great War was not simply an end as far as internationalism was concerned: it marked the beginning, continuation or transformation of internationalist commitments.

,

  The Gentle Civilizer of Nations: The Rise and Fall of International Law 1870-1960, Cambridge: Cambridge University Press, 2001, pp. 39-41. On institutions funded by Solvay, see L. VIRE, « La 'Cité Scientifique' du Parc Léopold à Bruxelles », Cahiers Bruxellois, vol. 19, 1974, pp. 86-180; K. WILS and A. RASMUSSEN, « Sociology in a Transnational Perspective: Brussels, 1890-1925 », Revue Belge de Philologie et d'Histoire, vol. 90, no. 4, 2012, pp. 1273-97. 7 M. HERREN, Hintertüren zur Macht: Internationalismus und modernisierungsorientierte Außenpolitik in Belgien, der Schweiz und den USA, 1865-1914, Munich, Oldenbourg, 2000. 8 For a range of examples on this, see D. LAQUA, The Age of Internationalism (op. cit.), chapters 3, 4 and 5. 9 On cultural movements, see N. AUBERT, P.-Ph. FRAITURE and P. MCGUINESS (eds), From Art Nouveau to Surrealism: Belgium Modernity in the Making, London, Legenda, 2007. On the Catholic case, albeit with a focus on the period before the fin de siècle, see V. VIAENE, Belgium and the Holy See from Gregory XVI to Pius IX, 1831-1859: Catholic Revival, Society and Politics in 19th-Century Europe, Institut belge de Rome, Brussels, 2001. 10 For a plethora of examples, see M. GEYER and J. PAULMANN (eds), The Mechanics of Internationalism: Culture, Society, and Politics from the 1840s to the First World War, Oxford, Oxford University Press, 2001.

11

H. PIRENNE, Histoire de Belgique, vol. 7 (op. cit.), p. 391.

J. CARLIER, Moving Beyond Boundaries: An Entangled History of Feminism in Belgium 1890-1914, PhD thesis, Ghent University, 2010, p. 453.

For the ABPE's activities, which involved work with children and the organisation of school festivals, see N. LUBELSKI-BERNARD, « Les mouvements et les idéologies pacifistes » (op. cit.), pp. 415-6.

E. GUBIN, « Eugénie Hamer » (op. cit.), p. 305.

N. LUBELSKI-BERNARD, « Le partisan de la paix », in H. Goffin (ed.), Henri La Fontaine, un Prix Nobel de la Paix, 1854-1943 : Tracé(s) d'une vie, Mons, Mundaneum, 2002, p. 72.

See Fried's diary entry of 11 January 1915: A. H. FRIED, Mein Kriegstagebuch: 7. August 1914 bis 30. Juni 1919, Bremen, Donat, 2005, p. 64. The episode is also mentioned in V. GROSSI, Le pacifisme européen: 1889-1914, Brussels, Bruylant, 1994, p. 395.

On the challenges for peace activism in wartime Germany, see J. D. SHAND, « German Pacifists and their Government during World War I », Journal of Contemporary History, vol. 10, no. 1, 1975, pp. 95-108.

Eugénie Hamer: Female Pacifism

Relatively little is known about Eugénie Hamer's wartime experiences. A brief entry in the Dictionnaire des Femmes Belges suggests that she remained in Belgium and cared for her brother, who had been injured in combat with the Germans [START_REF] Gubin | Eugénie Hamer[END_REF] . Despite the lack of biographical detail, Hamer's institutional attachments shed light on the tribulations of women's internationalism during the war. As secretary of the ABPE, her activism played out within the wider arena of Belgian women's activism. This commitment was more than just a national matter: it was shaped by diverse influences from abroad [START_REF] Carlier | Forgotten Transnational Connections and National Contexts: An 'Entangled History' of the Political Transfers that Shaped Belgian Feminism, 1890-1914[END_REF] . The outbreak of war, however, led many militantes to concentrate on national concerns. Carlier has diagnosed « an upsurge of patriotism and anti-German sentiment, which affected even the most convinced pacifists among them » [START_REF] Carlier | Entangled Feminisms[END_REF] . One example was the foundation of the Patriotic Union of Belgian Women (Union Patriotique des Femmes Belges) shortly after the German attack -a body that placed the activities of different women's groups at the service of the nation [START_REF] Carlier | Moving beyond Boundaries[END_REF] . The leading Belgian suffragist Jane Brigode became a key figure in this organisation. Having previously been involved in the International Woman Suffrage Alliance, she rejected the idea of a meeting with German feminists even after the war had ended [START_REF]Letter from Jane Brigode to Aletta Jacobs, 22 and 24[END_REF] . As Christa Hämmerle, Oswald Überegger and Brigitta Bader Zaar have put it, the First World War « contested the internationalism of the women's movement and exerted a great strain on the latent tension between national interests and the peace agenda within international women's organizations » [START_REF] Ch | Women's and Gender History of the First World War -Topics, Concepts, Perspectives[END_REF] .

These developments make it particularly striking that Hamer participated in the International Congress of Women at The Hague. Taking place from 28 April to 1 May 1915, this event was a major episode in the history of women's internationalism. The Dutch feminist Aletta Jacobs had launched this initiative after the planned Berlin congress of the International Woman Suffrage Alliance had been cancelled. The outcome was impressive: the event at The Hague brought together over 1,100 women from belligerent Conference », one of their demands resembled the ideas that La Fontaine articulated at around the same time [START_REF]International Congress of Women at The Hague[END_REF] .

Another outcome was the creation of the International Women's Committee for a Permanent Peace. Initially, both Hamer and Sarten were listed on its letterhead 90 . Furthermore, several activists from neutral nations became designated envoys who were charged with conveying the congress demands to national governments. David Patterson has examined this « citizen diplomacy » which was based on « the idea of private citizens calling on the heads of European governments » [START_REF] Patterson | The Search for Negotiated Peace[END_REF] . The American members of the Women's Peace Party played a key role in this endeavour. One leg of their journey took them to Le Havre, the site of the Belgian government-inexile. There, they met with Julien Davignon, the Belgian Minister of Foreign Affairs, whom they described as « a sad, gentle person » [START_REF] Hamilton | At the War Capitals[END_REF] . A subsequent report portrayed the meeting as cordial, recording the statesman as saying that « Belgium would rather have the enemy leave their country as the result of negotiations than have the armies fighting over it a second time » 93 .

While such comments seem to suggest ongoing dialogue even beyond The Hague, the German occupation was a complicating factor. Wilmers has noted that the Gazet van Brussel provided positive coverage of the congress, but pointed out that this could have been caused by a misunderstanding: the Gazet was a Flemish publication funded by the Germans and its authors may have erroneously perceived the congress as a pro-German initiative 94 . From the other side, nationally-minded Belgian feminists maintained a cautious distance from the International Women's Committee for a Permanent Peace. For instance, when the organisation contacted Élise (Soyer) Nyst of the National Council of Belgian Women (Comité Nationale des Femmes Belges) in late 1915, Nyst responded by saying that the National Council was too busy addressing the miseries of Belgium and thus indicated that it would be difficult for her to participate. She claimed that, instead of her own organisation, the ABPE would provide the Belgian response to the International Women's Committee -yet at the time, apparently no letter from the ABPE reached the activists in The Hague [START_REF]Letter from Élise Nyst (Soyer-Nyst) to Rosa Manus[END_REF] . Likewise, when Aletta Jacobs recorded the outcome of a survey among national affiliates of her organisation in March 1917, no Belgian information featured [START_REF]Letter from Aletta Jacobs to Jane Addams[END_REF] . This is not to say that the rupture was permanent. In 1921, the Women's International League for Peace and Freedom (WILPF) -the body that had developed out of the Women's Committee for a Permanent Peace -gained a