Franc ¸ois Charoy Karim Dahman
email: karim.dahman@loria.fr

Claude Godart
email: claude.godart@loria.fr

From Business Process to Component Architecture: Engineering Business to IT Alignment

Keywords: Unidirectional Model Transformation, Business-IT Alignment, BPMN, SCA, Conceptual Mapping, ATL

Maintaining the alignment between the Business and IT is of high strategic relevance in today's enterprise roadmap. In this paper, we follow our previous assumption that this alignment will be better maintained if we are able to ensure a clear conceptual alignment between the Business Processes and the Software Architectures. As our aim is to provide an environment that would flawlessly support evolutions of the processes or of the architecture while maintaining this alignment, we build on the formal foundation that we have developed to ensure it and shows how it can be actually developed with current Model Driven Engineering technologies.

I. INTRODUCTION

For any enterprise that aims to conduct a successful Business, being able to model its architecture is now an important asset. Furthermore, being able to relate this business architecture to its supporting Information Technology (IT) is recognized as a driver for the efficiency of enterprise computing resource management. One of the claimed goal for the integration between the business dimension and the IT dimension is to allow the agility in conducting the business, and adapting it to evolving business demands. The challenges to enforce this alignment from the business strategic perspective to the IT still need to be addressed. New approaches promoted through Service Oriented Computing (SOC), Business Process Management (BPM) and Enterprise Architecture are meant to be efficient enablers of this alignment and of its maintenance. Among these three disciplines, the BPM along with the SOC paradigm have an interesting quality. The BPM provides a direct bridge with almost no transformation between analysis, design, implementation and execution. Moreover, the SOC is supported by the Service Oriented Architecture (SOA [START_REF] Papazoglou | Serviceoriented computing: State of the art and research challenges[END_REF]) architectural foundation, and has emerged as a new computing paradigm for designing, building and using software applications to support business processes. The Business Process Modeling Notation (BPMN 2.0 [START_REF]Business Process Model and Notation 2.0, Beta 1[END_REF]) standard-related practices try to sustain this bridge by letting business analysts and application architects work on the same readily understandable model to obtain a (business process driven) software system.

We are still far from the streamlined experience where we could derive deployable software artifacts with sound architectural foundation from a BPMN collaboration diagram. This is even more true when we need to take into account the deployment topology of heterogeneous, distributed and continuously changing IT environments to support the process executions. Our goal, however, is to show that it would be possible to automate that business production line from the service-enabled process dependencies into the architectural software settings and its maintenance, while using the industry recognized standards like the BPMN and the Service Component Architecture (SCA 1.1 [START_REF]SCA Assembly Model Specification 1.1, Open SOA[END_REF]). In a previous work [START_REF] Dahman | Generation of Component Based Architecture from Business Processes: Model Driven Engineering for SOA[END_REF], we have shown that its was possible to leverage the Model Driven Engineering (MDE) to generate SCA models from a subset of the BPMN models. The contribution of this paper is to demonstrate how these theoretical results can be implemented using current model transformation technologies. For this purpose, we have developed an ATLAS Transformation Language (ATL [START_REF] Jouault | Towards incremental execution of atl transformations[END_REF]) transformation chain that is able to generate canonical SCA artifacts from a BPMN collaboration model. We have also identified how this technology will be an issue for our future development to maintain the Business Processes/SOA Assets alignment as it does not support incremental transformations. This is an important problem regarding the goal that we are pursuing: being able to keep the consistency and to maintain the alignment of the processes with the software architectures in every directions (i.e., round tripping), thus supporting agility from the realistic business settings with complex IT environments.

The next section of this paper is a short reminder of our previous work. Section III describes the theoretical result for the implementation of our ATL transformation chain in the Eclipse development environment [START_REF] Steinberg | EMF: Eclipse Modeling Framework 2.0[END_REF]. In Section IV, we situate our work through the related research and discuss the limit that we have encountered during this work. The last part conclude that work with a brief evaluation of other alternatives.

II. BACKGROUND AND FORMAL FOUNDATIONS

Typically, the Business Process Modeling combines graphical and textual annotations to specify the business process models that are decoupled from their supporting technical and software architectures. Several languages can be used to specify the business service interactions at different levels of abstraction [START_REF] Dumas | Service-enabled process management[END_REF]. Specially, the BPMN collaboration models express and put in logical relation the exchanges between the internal processes of service-enabled business networks. They aim at coordinating an explicit exchange of information through automated service interactions under the control of a single endpoint, called orchestration process [START_REF] Papazoglou | Serviceoriented computing: State of the art and research challenges[END_REF]. In the SOC those processes are mapped into models that describe services in a uniform and technology-independent way. At this lower abstraction level, i.e., the IT level, they describe the configuration of the so-called SCA assembly models which are organized in a SOA. The SCA assemblies modularize and compose service-enabled business functions in a manner that is decoupled from their application code. The SCA provides an Architecture Description Language (ADL) that offers means to define platform independent component kit architectures and a path from the business goals to the program code (e.g., executable process languages). With a graphical notation support, it describes composites of components, their connections and other related artifacts which specify how the component functions are externally consumed and/or offered.

The SOC extends the Component Based Development paradigm which states that applications expose their functionality as services in a uniform and technology-independent way such that they can be provided and invoked over looselycoupled architectures. Consequently, the service-enabled business functions can be implemented as components with remotely published interfaces in a network. Our previous work has introduced a MDE approach for the automated generation of (target) canonical SCA assembly models from (source) core BPMN collaboration models, and specified relations among their metamodels as conceptual mappings [START_REF] Dahman | Generation of Component Based Architecture from Business Processes: Model Driven Engineering for SOA[END_REF]. In our semantics, models are conform to a metamodel. As a part of this view, the models are viewed as assorted collections of typed objects with attributes, and typed links among the objects. The mapping between the heterogeneous BPMN and SCA models are viewed as rules that establish relations between the model types. We refer to the program executions that implement conceptual mappings as transformations. Figure 1 depicts an example of a model transformation which will be used through the reminder of this paper. It illustrates few situations that occur when the "task-driven process logic" has to be transformed into the "component composition logic". In the next section, we present the syntax of those models.

A. The BPMN and SCA Model Syntaxes

At the BPMN level, the processes are focused on the composition of services in a business driven-fashion, i.e., the orchestration process, and in that sense the business services become process activities. Moreover, the processes become composite business services that orchestrates other services and the business service networks are modeled as BPMN collaborations. A collaboration refers to the interactions between a collection of participants which represent the business entities or roles. They form a business service network and define the business process logic of each partner pertaining to a domain being modeled. The BPMN refers to a service orchestration as a participant's private process. Consider, the wellknown BPMN dealing network example [START_REF]Business Process Model and Notation 2.0, Beta 1[END_REF] depicted in Figure 1. In this business service network, a retailer provides an ordering service to a customer partner. In order to provide this service, the retailer establishes business links with other partners (e.g., scheduler, invoicer, and a shipper), and orchestrates their exposed services: scheduling, invoicing, and shipping. To sustain the separation of concerns in the service "orchestration logic" [START_REF] Rosen | Applied SOA: Service-Oriented Architecture and Design Strategies[END_REF], the retailer participant's private process is modeled with different sub-roles (e.g., order, schedule, invoice and shipment). Those roles contain tasks which invoke or provide operations for a single external service provider (i.e., relative to the retailer). The collaboration specifies the behavioral and architectural views of the business structures and their participant roles. The business links between participants are modeled as conversations that capture the service contracts. Formally, we define those models as below.

Definition 1 (Source Core BPMN Collaboration Model):

A source core BPMN collaboration model is a tuple s = (P, R, A, A , A , E, F , conv, H, L) where P is a set of participants which can be partitioned to disjoint sets of sub-roles R and interaction tasks A which can be partitioned into disjoint sets of send tasks A , receive tasks A , E ⊆ P × P is a participant association relation, F ⊆ A × A is the sequence flow relation between the tasks, conv :

∪ p∈P A p → ∪ p∈P A p is an injective function which maps interaction tasks, H = {(a, a ) ∈ A p × A p | ∃ p,p ∈P conv(a) = a } is the conversation relation, and L ⊆ R × A is a process relation.
Likewise, when mapped to the SCA space, the services become components. The processes are executed by servicecomponents that contain the effective implementation artifacts. The inter-component interactions are conceptually similar to the inter-process invocations. Consequently, the conversations between processes can map to the connectors between components. It must to be noticed, that we intentionally hide definition of the rest of BPMN constructs shown in Figure 1 (e.g., events, sequence flows and gateways), since those types have not conceptually equivalent counterpart types in SCA as explained in Section II-B. to generate sound component compositions we have introduced in [START_REF] Dahman | Generation of Component Based Architecture from Business Processes: Model Driven Engineering for SOA[END_REF] a technique that emphasizes the separation of service modeling concerns between the BPMN design space and the SCA level. This technique, which we called orchestration process partitioning, is intended for avoiding the straight mapping of the inter-task dependencies to the component connectors. As shown in Figure 1, it transforms the inter-task control flow of a single orchestration process with different roles, e.g., retailer, into a new collaboration between separated processes, with singular roles. Also, it decomposes monolithic "taskdriven logic" into functionally equivalent decoupled logics. Each resulting participant, e.g., order, schedule, invoice and shipment, contains its own private process with additional synchronization tasks.

Due to the lack of space, we do not give details of the partitioning algorithm. Those processes directly interact with each other with additional conversation. Formally, for any p ∈ P, the subset of interaction tasks A p that have conversations with the same external participant (i.e., service denoted p ∈ P)

is denoted A p p = {a ∈ A p ∪ A p | ∃a ∈ A p aHa }.
By applying the orchestration partitioning algorithm to its process, i.e., denoted L p ⊆ R p × A p , we obtain a set of participants P where P = R p and ∀ p ∈P | ∃ p ∈P A p = A p p ∧ R p = {p }. Each obtained participant, i.e., "process partition" denoted p , includes only a subset of the tasks that invoke (resp., provide) operations on a same service provider, i.e. denoted p (resp., consumer). Those partitions represent "proxy" orchestrations that are related to each external service. They are fine-grained internal services composing the initial service (i.e., relative to the initial participant p) and they are matched up with p through participant associations, i.e., E ⊆ ∪ p∈P × ∪ p ∈P . In this case, we refer to the initial participant as an associated participant. The orchestration partitioning ensures a more manageable component architecture and adds a clear architectural view about how fine-grained services are composed, that the BPMN per se fails to capture.

In the SCA, the assembly models logically modularize and compose components in a manner that is decoupled from their code. A component can be a composite (i.e., an assembly of components glued together using some "composition logic") or atomic when it is considered without its inside structure. The components expose their provided ports, i.e., called services, and require (i.e., or discover) other services by means of references. They are configured to interact with the other components through the connectors, i.e., called wires. Also, the callbacks can be defined for services and references when the components play per se both the service consumer and provider roles. Finally, each component contains the implementation with an appropriate technology of the process specified by the mapped participant's orchestration. We define those models to be used for the further formal foundations of the model transformation which are given in the next section.

Definition 2 (Target Canonical SCA Assembly Model):

A target canonical SCA assembly model, i.e., assimilated to a composite, is a tuple t = ( B,M,N ,C,O,Q,K,G,J ,I,R,V,W) where B is a set of sub-composites which can be partitioned to disjoint sets of composite services M and composite references N , C is a set of components which can be partitioned into disjoint sets of component services O and component references

Q, K is a set of callbacks, G ⊆ (M ∪ N ) × K is the composite callback relation, J ⊆ (O ∪ Q) × K is the component I is the of implementations, R ⊆ (M × O) ∪ (N × Q) is the promotion relation, V ⊆ C × B is the implementation as composite relation, and W ⊆ (M ∪ Q) × (N ∪ O) is the wire relation.

B. The BPMN to SCA Conceptual Mapping

Before we delve into the formal details, a look at the general model transformation problem is needed. Given two metamodels S and T , the model-to-model transformation, denoted trans map : S → T , is a partial function that takes a source model s in S and produces a target model t in T . The source-to-target types correspondences are defined by a partial function, denoted map, which is based on the semantics of the source core BPMN collaboration and the target SCA assembly types. This means that only the source model objects with types that has proper conceptual mapping into target types are transformed. For example, only the tasks that specify service interactions (i.e., send or receive) are transformed. The other constructs such as gateways and events are not relevant for sketching the component assembly, but, define functional aspects of the component implementation. Moreover, we define an index function as follows:

∀ p,p ∈P | ∃ a∈Ap,a ∈A p , aHa , index(a) = initial p if a ∈Ap | a ∈ prev * (a) and index(a) = f inal p if a ∈Ap | a ∈ next * (a).
This function is used to differentiate the tasks in the service interaction patterns [START_REF] Van Der Aalst | Service Interaction: Patterns, Formalization, and Analysis[END_REF] in the following definition. The functions denoted prev * (a) = {a ∈ A p | a F * p a} and next * (a) = {a ∈ A p | aF * p a } give the set of all direct and transitive predecessors and successors of a task a, where F * p is the reflexive transitive closure of F p . A static analysis of the process flow is considered to distinguish tasks in conversations. We formally define the mapping below.

Definition 3 (Collaboration to Composite Mapping):

Let s = (A, R, P, A , A , E, F , conv, H, L) be a well-formed and well-behaved source core BPMN collaboration model (i.e., given in Definition 1). s can be conceptually mapped to onto a target canonical SCA assembly model, i.e., assimilated to a composite map(s) = ( B,M,N ,C,O,Q,K,G,J ,I,U,V,W) where

• B = p∈P {p | ∃ p ∈P pEp }, i.e., associated participant to composite, • M = p∈P {a ∈ A p | ∃ p ,p ∈P pEp ∧ index(a) = initial p }, i.e.
, initial receive task to composite service,

• N = p∈P {a ∈ A p | ∃ p ,p ∈P pEp ∧ index(a) = initial p }, i.e., initial send composite reference, • C = P \ p∈P {p | ∃ p ∈P pEp }, i.e., participant to component, • O = p∈P {a ∈ A p | p ∈P pEp ∧ ∃ p ∈P index(a) = initial p }, i.e.

, initial receive task to component service,

• Q = p∈P {a ∈ A p | p ∈P pEp ∧ ∃ p ∈P index(a) =
initial p }, i.e., initial send task to component reference, Note that we assume the well-formedness of the source models and its well behavedeness. It means they are consistent with the structural and the behavioral requirements of service interaction specification, e.g., defined in [START_REF] Van Der Aalst | Service Interaction: Patterns, Formalization, and Analysis[END_REF]. For the minimal correctness requirements on the structure of the processes we follow [START_REF] Dijkman | Semantics and analysis of business process models in bpmn[END_REF], e.g., there is a single start event, there is one or more end events, and every process task is on a path from the start event to an end event. Due to lack of space, we refer to [START_REF] Léger | Reliable Dynamic Reconfigurations in a Reflective Component Model[END_REF] for detailed structural requirements on the SCA models. Since the BPNM participants map into SCA components, then, after the orchestration partitioning, the obtained participant associations between the new participants map into the implementations as composites. For example, Figure 1 shows the mapping of participants resulting from the retailer's process partitioning. The associated participant is mapped to a component. The collaboration obtained after the partitioning maps into the retailer composite which is attached to the implementation of the initial retailer component. Recursively, each obtained sub-participant, e.g., order, schedule, invoice and shipment, is mapped onto a component, and it is placed within the implementing composite. The process of each subparticipant maps to a single component implementation. This allows different technologies to be used for each process implementation. It has to be noticed that we do not make recommendations on the technology usage.

• K = p∈P {a ∈ A p ∪ A p | ∃ p ∈P,a ∈Ap a ∈ next * (a ) ∧ index(a ) = initial p ∧ index(a) = f inal p }, i.e.

, final receive task or final send task to callback,

• G = p∈P {(a, a ) ∈ A p × A p | ∃ p ,p ∈P pEp ∧ a ∈ prev * (a ) ∧ index(a) = initial p ∧ index(a ) = f inal p }, i.e.

, associated receive task relation to composite callback relation,

• J = p∈P {(a, a ) ∈ A p × A p | p ∈P pEp ∧ ∃ p ∈P a ∈ prev * (a ) ∧ index(a) = initial p ∧ index(a ) = f inal p }, i.

III. BPMN TO SCA MODEL TRANSFORMATION

In the previous section, we have introduced the conceptual mapping for the transformation of canonical SCA assembly models from core BPMN collaboration models. This section performs a more through investigation on the implementation of the transformation code. In order to implement the transformation of the model artifacts, we use the ATL transformation chain which is depicted in Figure 2. The ATL is integrated in the Eclipse development environment and can handle models based on the core Eclipse Modeling Framework (Ecore [START_REF] Steinberg | EMF: Eclipse Modeling Framework 2.0[END_REF]). It also provides support for models using EMF-based UML profiles. In our proof-of-concept prototype, the BPMN and SCA metamodels are created using the Ecore. The BPMN diagrams and the SCA definitions metamodels are specified in the eXtensible Markup Language Metadata Interchange (XMI). Rather than using intermediate model facilities [START_REF] Mos | Multi-layer perspectives and spaces in soa[END_REF], we advocate a direct transformation chain that starts off from a BPMN XMI file containing the source core BPMN collaboration model. Then, its orchestrations are partitioned. Subsequently, this model is transformed into a target canonical SCA assembly model resulting in XML files which contain the Service Component Definition Language (SCDL [START_REF]SCA Assembly Model Specification 1.1, Open SOA[END_REF]) of the mapped composites, i.e., the particular ADL of the SCA. An ATL-code is composed of rules describing how to generate the objects of the target models. It is compiled into the ATL bytecode and then executed by the ATL virtual machine [START_REF] Jouault | Towards incremental execution of atl transformations[END_REF]. As a simple running example, consider the following BPMNtoSCA ATL program, i.e., the module. It defines four rules from the conceptual mapping given in Definition 3. Those rules uses the simplified BPMN and SCA metamodels shown in Figure 2. The ATL is a hybrid modelto-model transformation language that supports both declarative and imperative constructs [START_REF] Biehl | Literature Study on Model Transformations[END_REF]. The preferred style is declarative, which allows simpler implementation for relatively simple conceptual mappings. However, imperative constructs are provided so that some not trivial mappings to be handled declaratively can still be specified. Roughly speaking, the ATL program transforms a collaboration to a composite and each participant of the collaboration to a component of the corresponding composite. Also, the rules map the send and the receive task in a straightforward manner to component services and references. The order of the rule execution is determined automatically, with the exception of lazy rules, which needs to be called explicitly. The helper functions provide imperative constructs.

In order to ensure the consistent BPMN-to-SCA mapping, we partition the service-enabled business process into smaller decoupled service-components with separate concerns. The orchestration process partitioning is written with imperative constructs (i.e., not presented in the above ATL-code due to lack of space). It provides a better view on the dependencies between the component inside the application being modeled (e.g., order, schedule, invoice and shipment within retailer in Figure 1) and their relationships with the outside of the system (e.g., customer, scheduler, invoicer, and a shipper). Also, it makes the overall component architecture more robust and flexible for the later business process or IT evolutions. Eventually, realizing some change in a specific single business service contract brings into play only a part of the component configuration architecture. Finally, it becomes possible only when looking at this SCA architecture to localize the concerned parts to be changed, without spying on the opaque application code. It is undeniable, however, that the flexibility to adapt the processes in order to respond to evolving business needs is the most relevant trend in the MDE success.

IV. RELATED WORK

In order to align the Business and IT capabilities, various organizational considerations need to be taken into account [START_REF] Chen | From software architecture analysis to service engineering: An empirical study of methodology development for enterprise soa implementation[END_REF], [START_REF] Levi | A goal-driven approach to enterprise component identification and specification[END_REF]. In this paper, we focus on the Business-IT alignment through the business processes, particularly, on the generation of the software architectures from service-enabled (business process driven) system specifications. Several languages can be used to specify the service interaction models at different levels of abstraction [START_REF] Dumas | Service-enabled process management[END_REF]. Using the BPMN 2.0 [START_REF]Business Process Model and Notation 2.0, Beta 1[END_REF] can provide the sufficient conceptual information needed to specify a complex service-enabled system in a cross-organizational setting. Likewise, the SCA [START_REF]SCA Assembly Model Specification 1.1, Open SOA[END_REF] provides a framework for creating software solutions based in a multi-language and multi-platform environment that are based on complex IT environments. As an alternative to the BPMN along with the SCDL, one could use UML Activity Diagrams and Sequence Diagrams, which offer comparable features along with any other ADL. However, as the UML is neither fully servicecentered, nor business process-oriented, it is necessary to provide alternative methods to design the business process logic independently of their implementation infrastructure. Thus, the MDE techniques needs to address the gap in existing UML modeling methodologies for the system engineering with a Service Dominant Logic [START_REF] Chen | From software architecture analysis to service engineering: An empirical study of methodology development for enterprise soa implementation[END_REF], [START_REF] Levi | A goal-driven approach to enterprise component identification and specification[END_REF].

In [START_REF] Mos | Multi-layer perspectives and spaces in soa[END_REF], the authors present a MDE scenario that uses the Eclipse SOA Tools Platform Intermediate Metamodel. The scenario starts off with a business process specified in the BPMN, leading to an intermediate model and resulting in a SCA model [START_REF]SCA Assembly Model Specification 1.1, Open SOA[END_REF]. The approach is promising, however, the absence of accurate mappings between the two metamodels makes the model transformation not viable. First, it requires further manual adaptation to reflect the initial process requirements because the BPMN per se neither specifies the roles (e.g., consumer or provider) that participants are expected to play in a business collaboration. Of course, adapting the generated SCA configurations necessarily leads to their misalignment with the business process layer, and implies design decision losses. Second, the provided automated incremental transformation is fictional, since from the initial mapping, the source constructs are mapped to conceptually different target elements. Thus, providing consistency management over this approach turns out to very challenging endeavor in practice. Furthermore, the change propagation is a major use case for the MDE. When a source model is changed and that a transformation has previously generated a corresponding target model, it is necessary to keep the models synchronized. The model transformation languages [START_REF] Biehl | Literature Study on Model Transformations[END_REF], specifically the ATL [START_REF] Jouault | Towards incremental execution of atl transformations[END_REF], cannot work well here. It supports a mode for in-place transformation, called the refining mode [START_REF] Jouault | Towards incremental execution of atl transformations[END_REF], but it does not support incremental model transformations: a complete source model is read and a complete target model is created. Thus, the manual changes in the target model are not preserved [START_REF] Xiong | Towards automatic model synchronization from model transformations[END_REF]. Morevover, the Query/View/Transformation (QVT) is a standardized language for model unidirectional transformations. Some of the issues for the QVT usage was raised in [START_REF] Stevens | Bidirectional model transformations in qvt: Semantic issues and open questions[END_REF]. The ATL supports only unidirectional transformation code. First, it requires to explicitly write the synchronization code to deal with each kind of update on each type of assorted models. Second, the complexity of each combinatorial change mapping is inherently compounded with decisions regarding the potential information loss or gain related to different levels of model's expressiveness. They make the synchronization code much complex, particularly, when not all the source model elements correspond the to target model elements. For example, it is necessary to revise both the SCA definitions and their implementations, just to make a minor change on the service interaction patterns [START_REF] Van Der Aalst | Service Interaction: Patterns, Formalization, and Analysis[END_REF] at the BPMN level.

V. SUMMARY AND OUTLOOK

In this paper, we have presented a development scenarios for the SOC, where business process specifications drive component architectures that are organized in a SOA. At the design-time, the business analyst focus on the modeling of task-driven and service-oriented logics without being bothered by any implementation-specific configuration information. The introduced conceptual mapping rules enable the transformation of BPMN collaboration models into canonical SCA assembly models. The later models describe and guide the final system deployment architecture and its implementation. Thus, the reuse of some existing software applications as well as creating new ones to be reused in other system parts become more evident for the architects. At the execution-time, the assembly models are instantiated for the SCA runtime environments and benefit from those frameworks for deployment and monitoring. Since there is no mean of control flows between the SCA components, then, it seems that some BPMN behavioral aspects have no counterparts in the SCA. However, other semantics can be defined in the SCA components. Therefore, we want to enlarge our approach by transforming other BPMN constructs to non-standard SCA elements for example for the implementation of non-functional requirements.

The experimental results for the BPMN-to-SCA transformation with the ATL are encouraging, and the MDE approach seems very promising, however, it still needs to be validated in a real-scale case studies. The integration of our ATL chain in the Eclipse SOA Tools Platform [START_REF]Eclipse soa tools platform project[END_REF] is in development. Furthermore, the (full) round-tripping between the business processes and the SOA is essential to rapidly realign the IT to accommodate changing business conditions. Consequently, striving for further alignment via service pattern-based techniques, and making SOA development more tractable to reconfigure architectures without disrupting the functional capabilities of the implementations remain as a future work.

Fig. 1 .

 1 Fig. 1. BPMN-to-SCA transformation example and languages constructs.

  e., associated send task relation to component callback relation,• I = p∈P {p | p ∈P pEp ∧ ∃ a∈Ap,r∈Rp rLa}, i.e.,process to implementation,• U = p∈P {(a, a ) ∈ (A p ×A p )∪(A p ×A p ) | ∃ p ,p ∈P pEp ∧ index(a) = initial p ∧ index(a ) = initial p }, i.e., associated task relation to promotion relation, • V = p∈P {(p, p ) ∈ P × P | ∃ p ∈P pEp }, i.e., participant association to implementation as composite, • W = p∈P {(a, a ) ∈ A p × A p | ∃ p ∈P index(a) = initial p ∧ index(a ) = initial p ∧ aHa }, i.e., conversation to wire.

Fig. 2 .

 2 Fig. 2. BPMN-to-SCA transformation ATL chain overview.

  module BPMNtoSCA; create OUT : SCA from IN : BPMN; helper context BPMN!Definitions def : CollaborationHasParticipants() : Boolean = if (self.getCollaboration(). participants.oclIsUndefined()) then false else true endif; helper context BPMN!Definitions def : getDefinitions() : BPMN!Definitions = self; helper context BPMN!Definitions def : getCollaboration() : BPMN!Collaboration = (self.rootElements -> select (e | e.oclIsTypeOf( CollaborationtoComposite { from d: BPMN!Definitions, s: BPMN!Collaboration to t: SCA!Composite(name <-s.name, component <-BPMN!Participant.allInstancesFrom('IN') -> collect(e | if not e.processRef.oclIsUndefined() thisModule.ParticipanttoComponent(e, d,e.processRef))} lazy rule ParticipanttoComponent { from d: BPMN!Definitions, p: BPMN!Participant, l: BPMN!Process to c: SCA!Component(name <if d.CollaborationHasParticipants()=true then p.name else d.getCollaboration().name endif, reference <-BPMN!SendTask.allInstancesFrom('IN')-> select(e | l.flowElements.includes(e))-> collect(e | thisModule.SendTaskToReference(e)), service <-BPMN!ReceiveTask.allInstancesFrom('IN') -> select(e | l.flowElements.includes(e))-> collect(e | thisModule.ReceiveTaskToService(e)))} lazy rule SendTaskToReference { from sen: BPMN!SendTask to ref: SCA!ComponentReference(name <-sen.name)} lazy rule ReceiveTaskToService { from rec: BPMN!ReceiveTask to ser: SCA!ComponentService (name <-rec.name)}

BPMN Collaboration Graphical Constructs

				Scheduler				Shipper
									Shipping
		Schedule	Request Product Scheduling
	Retailer	Shipment				Request Shipping Schedule	Receive Shipping Schedule	Send Shipping Schedule
		Order		Receive Order
		Invoice			Initiate Price Calculations		Complete Price Calculations
				Customer			Invoicer
	Dealing Network
									SCA Assembly Graphical Constructs
	StartEvent	EndEvent	SendTask ReceiveTask	Process Participant Pool	Fork/Join	Service or	Composite Component	Implementation
	Conversation	SequenceFlow	ConversationLink	Parallel Gateway	Reference Callback	Reference	Service	Wire

Retailer Invoicer Customer Target Canonical SCA Assembly Model Source Core BPMN Collaboration Model Dealing Network

	Scheduling
								Receive
								Product
							Scheduling
									Send Invoice
								Process
								Invoice
	Ordering
					Invoicing
			Partitioned Core BPMN Collaboration Model
					Dealing Network
	Schedule	Scheduling Start		Request Product Scheduling	Receive Product Scheduling		Scheduling End
	Shipment	Shipping Start	Scheduling	Request Shipping Schedule	Receive Shipping Schedule	Send Shipping Schedule	Shipping	Shipping End
			End					Intermediate
						Scheduling
						Start
	Order	Receive Order			Shipping Start	Shipping End		Send Invoice
					Invoice	Invoicing
					Start		End
	Invoice	Start Shipping Invoice Intermediate	Initiate Calculations Price	Complete Price Calculations	Process Invoice	Invoicing End
						Promotion

Retailer Invoice Order Schedule Shipment Shipper Scheduler


Luca Caricchi
email: l.caricchi@bristol.ac.uk

Anne Pommier

Mattia Pistone

Jonathan Castro

Alain Burgisser

Diego Perugini

Strain-induced magma degassing: Insights from simple shear experiments on bubble bearing melts

Keywords: Magma deformation, strain-induced degassing, bubble deformation, obsidian banding

Experiments have been performed to determine the effect of deformation on degassing of bubble bearing melts. Cylindrical specimens of phonolitic composition, initial water content of 1.5 wt.% and 2 vol.% bubbles, have been deformed in simple shear (torsional configuration) in an internally heated Paterson-type pressure vessel at temperature of 798-848 K, 100-180 MPa confining pressure and different final strains. Micro-structural analyses of the samples before and after deformation have been performed in two and three dimensions using optical microscopy, a nanotomographer and synchrotron tomography. The water content of the glasses before and after deformation has been measured using Fourier Transform Infrared Spectroscopy (FTIR). Up to a total applied strain of γ∼2 the bubbles record accurately the applied strain, whereas at higher strains (γ∼10) the vesicles become very flattened and elongated in the direction of shear. The residual water content of the glasses remains constant up to a strain of γ∼2 and decreases to about 0.2 wt.% at γ∼10.

Results show that strain enhances bubble coalescence and degassing even at low bubble volume fraction. Noticeably, deformation produced a strongly water undersaturated melt. This suggests that degassing may occur at great depths in the volcanic conduit and may force the magma to become super-cooled early during ascent to the Earth surface potentially contributing to the genesis of obsidian.

Introduction

The style and rate of degassing during magma ascent in volcanic conduits is one of the main factors controlling eruption dynamics. As an example, the transition from highly explosive to effusive eruptions, as recently observed at Chaitén volcano (Chile; [START_REF] Castro | Rapid ascent of rhyolitic magma at Chaiten volcano, Chile[END_REF], may result from the efficient degassing of high viscosity magmas through a permeable bubble network. Magma experiences large shear deformation along conduit walls during ascent to the surface, a process that has been proven to strongly enhance bubble coalescence and favour magma degassing [START_REF] Rust | Determining flow type, shear rate and shear stress in magmas from bubble shapes and orientations[END_REF][START_REF] Okumura | Evolution of bubble microstructure in sheared rhyolite: Formation of a channel-like bubble network[END_REF][START_REF] Okumura | Magma deformation may induce non-explosive volcanism via degassing through bubble networks[END_REF]. Previous experimental studies carefully investigated the effect of strain and bubble content on connectivity showing that long-range bubble connectivity increases as strain and bubble volume fraction increase [START_REF] Okumura | Evolution of bubble microstructure in sheared rhyolite: Formation of a channel-like bubble network[END_REF][START_REF] Okumura | Magma deformation may induce non-explosive volcanism via degassing through bubble networks[END_REF]. The achievement of a connected network of bubbles may provide pathways for the gas to migrate through the magmatic mass, thus enhancing significantly magma degassing.

Although a number of works shed new light on the possible processes associated with magma degassing, there are still open questions about the mechanisms responsible for removal of the gas phase from magma bodies (e.g. [START_REF] Yoshimura | Diffusive dehydration and bubble resorption during open-system degassing of rhyolitic melts[END_REF].

In particular while it is intuitive that a connected network of bubbles would favour degassing, it is not clear which process may act to preserve this network open for sufficient time span to release a significant amount of gas from the magma. [START_REF] Yoshimura | Diffusive dehydration and bubble resorption during open-system degassing of rhyolitic melts[END_REF] envisage that the transfer of gas from melt to an interconnected degassing path is mainly controlled by H 2 O diffusion in the melt phase, which, in turn, is controlled by water concentration gradient and the pressure difference between the connected gas path and the magma. As a result, diffusive degassing requires significant durations (hundreds of hours; [START_REF] Yoshimura | Diffusive dehydration and bubble resorption during open-system degassing of rhyolitic melts[END_REF] to explain the formation of degassed and bubble-free bands (2-3 mm in thickness) observed in obsidians [START_REF] Castro | Vesiculation rates of obsidian domes inferred from H2O concentration profiles[END_REF]. Other processes occurring over shorter timescales should therefore play an active role in the degassing history of ascending magmas.

Here we experimentally investigate how strain/deformation induces and enhances the transfer of gas from a magma having only a modest quantity (<5%) of bubbles and at pressure conditions appropriate for magma in the deep plumbing system (4-6 km). This contrasts with previous studies that investigated the loss of gas from magmas with relatively high volume fraction of bubbles (e.g. Burgisser and Gardner, 2005;[START_REF] Okumura | Evolution of bubble microstructure in sheared rhyolite: Formation of a channel-like bubble network[END_REF]. Focusing on magmas containing small amounts of bubbles is fundamental to constraining the maximum depth at which degassing can play a role in the dynamics of volcanic eruptions. The potential applicability of our results to better understand the genesis of obsidians is also discussed.

Experimental techniques

Synthesis of starting material

Pumices from the 3760 BP Avellino eruption [START_REF] Rolandi | The Avellino Plinian Eruption of Somma-Vesuvius (3760 Y Bp) -the Progressive Evolution from Magmatic to Hydromagmatic Style[END_REF] were finely ground and cold pressed in large volume stainless steel canisters (36 mm external diameter, 34 mm internal diameter and ca. 100 mm in length). The fine powders obtained from the pumices were isostatically pressed at 180 MPa and 1373 K in an internally heated pressure vessel (pressurized with Argon, 40 litres of heated volume). Temperature was held constant for 24 hours. Samples were cooled with a rate of about 60 K/min to 753 K; the cooling rate was subsequently decreased to 0.6 K/min down to room temperature. This procedure generated a crystal free glass while avoiding the formation of cooling cracks. The gas content of pumices, before the synthesis, was determined to be 2.44 wt.% by loss on ignition. This value is in agreement with the study of [START_REF] Signorelli | Pre-eruptive volatile (H2O, F, Cl and S) contents of phonolitic magmas feeding the 3550-year old Avellino eruption from Vesuvius, southern Italy[END_REF], in which the relative content of Cl, F, S and H 2 O was measured on the same rock used as starting material for our experiments. The water content of the glass after the synthesis, measured by FTIR, was 1.5±0.16 wt.%. The glass was imaged by 3D tomography and the bubble content was ca. 2 vol.%. At the pressure and temperature conditions of the synthesis, the silicate melt is undersaturated in volatiles [START_REF] Moore | An empirical model for the solubility of H2O in magmas to 3 kilobars[END_REF][START_REF] Signorelli | Pre-eruptive volatile (H2O, F, Cl and S) contents of phonolitic magmas feeding the 3550-year old Avellino eruption from Vesuvius, southern Italy[END_REF].

During cooling, the pressure decreased at about ~1.3 MPa/min while the sample temperature remained comparatively high and constant due to the dimension of the specimen. Water vesicles were thus likely generated upon cooling. The presence of some residual air in the canisters and its limited solubility in silicate melts [START_REF] Mysen | Solubility and solution mechanisms of NOH volatiles in silicate melts at high pressure and temperatureamine groups and hydrogen fugacity[END_REF] contributed to the nucleation and stabilization of the water vesicles. The gas bubbles present in the samples thus contain a mixture of air and water; the small volume fraction of bubbles makes the starting material suitable for the present experimental study.

(FIGURE 1)

Simple shear deformation experiments

Experiments were performed in a Paterson-type deformation apparatus in torsion configuration, which imposes a simple shear strain field [START_REF] Paterson | Rock deformation tests to large shear strains in torsion[END_REF]; Fig. 1A), at temperatures of 823 and 873 K and confining pressures of 100 and 180 MPa. In this configuration, the strain increases linearly from the centre to the outer portions of the samples [START_REF] Paterson | Rock deformation tests to large shear strains in torsion[END_REF]. Cylindrical specimens of 15 mm diameter and 10 mm length were drilled out from the canisters used for the synthesis. Samples were placed in the centre of a symmetrical assembly, of the same diameter of the specimen, comprised on both sides by an alumina disk (3 mm length), an alumina cylinder (50 mm length) and a zirconia stabilized ceramic cylinder (30 mm length; Fig. 1A). The experimental assembly was inserted in pure iron or copper tube (jacket; 250 μm wall thickness) for the experiments performed at 180 and 100 MPa respectively. Metallic jackets separate the sample from contact with the Argon gas, used as confining medium. The furnace was previously calibrated and maximum temperature variations of about 2 K were allowed along the sample length. The ceramics constituting the top part of the assembly, except for the disk in contact with the sample, were hollow and the central hole hosted a thermocouple used for temperature measurements. The thermocouple was connected to atmospheric pressure and consequently the hole was at 0.1 MPa during the runs. The surfaces of ceramic surrounding the sample were slightly rough, which allowed the gas released by the sample to flow between the metallic jacket and the ceramic disk and escape through the thermocouple hole (Fig. 1A andB). An additional degassing path was present in the core of the specimens where a cylindrical electrode for electrical conductivity measurements was placed, as explained in the following section. As such, this experimental configuration allowed us to study the effect of deformation on degassing.

Electrical conductivity measurements

Impedance measurements were planned and for this purpose the core of the specimens was drilled to host a 4 mm diameter cylinder of copper (Fig. 1A).

Unfortunately, the transmission of the electrical signal between the Impedance Gain Phase Analyzer was not continuous during the experiments, precluding a straightforward interpretation of the electrical response of the samples. The central electrode was nevertheless employed in all the experiments to maintain the same geometrical setup.

Analytical techniques (TABLE 1)

The chemical composition of the natural samples used to synthesize the starting material was analysed by X-Ray Fluorescence (XRF; Table 1) at the institute of Mineralogy and Petrology of ETH Zurich (Switzerland). The composition of the samples after the experiments was analyzed using a JEOL-JXA-8200 Electron Microprobe Analyzer (EMPA; Table 1) at ETH Zurich (Switzerland). EMPA analytical conditions were 15 kV acceleration voltage, 5 nA beam current and 15 μm beam diameter. Negligible compositional differences were detected before (XRF) and after (EMPA) the experiments (Table 1).

Fourier Transform Infrared Spectroscopy (FTIR)

The water content of glasses was measured by a Nicolet Magna 760 instrument connected to a Nic-Plan microscope [START_REF] Gaillard | The effect of water and fO(2) on the ferric-ferrous ratio of silicic melts[END_REF]. A globar SiC source, a MTC/A detector and a CaF 2 splitter were used for the measurements. Spectra were collected between 2000 and 7400 cm -1 with a 4 or 8 cm -1 resolution.

Measurements were acquired on a minimum of 5 points (spot size 80-100 μm) for each sample from the core to the outer portion of the specimens. Absorption coefficient for the 4470 cm -1 and 5210 cm -1 bands, and densities from [START_REF] Marziano | Equilibrium and disequilibrium degassing of a phonolitic melt (Vesuvius AD 79 "white pumice") simulated by decompression experiments[END_REF] were used to obtain the total water content from the FTIR spectra. Bubble spacing in the different samples (150-400 μm) was sufficient to allow for accurate measurement of the matrix glass.

X-ray tomography (TABLE 2)

Cylindrical cores of 2 mm outer diameter and lengths between 2 and 4 mm were drilled out from the starting glass and from the deformed samples. Tomographic scans of the experiment performed at the highest strain (γ =9.6) were acquired from a larger section of the sample (~7 mm by ~6 mm by ~3 mm). The longest side of the section was cut along the sample radius and, consequently, the applied strain increases towards the external portion [START_REF] Paterson | Rock deformation tests to large shear strains in torsion[END_REF].

Three-dimensional images were acquired using a Phoenix Nanotom 180 X-ray Nanotomograph (for samples PP117 int., Table 2) at the Institute of Earth Sciences of the University of Orleans (France) and at the TOMCAT beamline (for sample PP116, PP117, and starting material, Table 2; [START_REF] Stampanoni | Trends in synchrotron-based tomographic imaging: the SLS experience[END_REF] at the Swiss Light Source (Paul Scherrer Institut, Villigen, Switzerland).

Micro-tomography analyses were performed with the Phoenix Nanotom 180 by mounting the specimens on a carbon fibre rod with a thermoplastic adhesive. Samples were placed in the chamber and rotated by 360 degrees during acquisition. An operating voltage of 70 KeV and a filament current of 220 nA were applied. The distance between the sample and the X-ray source and between the X-ray source and the detector was 11.5 and 280 mm, respectively. 2400 2D images were acquired during sample rotation with a resolution of 2.05 μm per voxel (i.e. the smallest volume element of the regular grid in the 3D space). The 2D raw images were converted into 3D image stacks using a micro-cluster of four Personal Computers with the Phoenix 3D reconstruction software.

At the TOMCAT beamline 2001, raw projections were acquired for each scan with 20 KeV energy using a 10x magnification objective and an exposure time of 100 ms. For each scan 32 dark and 451 flat images were collected, thus substantially improving the signal to noise ratio. A LAG Ce 20 μm scintillator was used to convert X-ray photons to visible light, which was projected on a 14bit-CCD camera. The result was a 2048x2048 pixel image for each projection with a resolution of 0.75 μm per voxel. The ImageJ software was used to reduce noise in the tomographic image stacks and to convert them to binary format. The 3D visualization and analysis of the gas vesicles was performed using the open source software Paraview (http://www.paraview.org/) and Blob3D [START_REF] Ketcham | Computational methods for quantitative analysis of threedimensional features in geological specimens[END_REF], respectively.

We converted the reconstructed, grayscale image stacks to binary format with Image J software. We first applied an anisotropic diffusion filter to each image in the stack, thereby eliminating small (1-2 pixel) isolated noise. Thresholding was then performed by manually adjusting the threshold cutoff point on a grayscale value histogram (i.e. the grayscale threshold dividing pixels into either white and black color) whilst observing that the integrity of the bubble-glass margins, bubble shapes, and bubble walls was maintained as adjustments were made. Because the grey scale contrast between the voids (bubbles) and matrix (glass) is quite large, this procedure resulted in minimal degradation of bubble shapes and sizes. We estimate that errors associated with binarization of bubble size and connectivity are lower than 5% of the measured values.

The two analytical facilities were used according to availability. The TOMCAT scans were acquired at the SLS synchrotron for which a limited amount of time is assigned for each experiment. The availability of an in-house tomography apparatus in Orleans made possible the completion of the additional required scans.

(FIGURE 2)

Results

Although experiments were performed below liquidus temperature, no crystallization occurred because of the short duration of the experiments. In all the experiments an initial elastic response, represented by a steep increase of stress upon the application of the strain rate, was followed by a strain hardening stage (yielding) and flow at relatively constant stress (Fig. 2 A andB). A correction for the presence of the metallic jacket was applied using calibration measurements that characterized the shear strength of the metallic jacket at the same temperature and pressure range as that of the experiments.

Significant stress and temperature oscillations were observed during deformation at 100 MPa, whereas both the recorded signals were constant during the experiments at 180 MPa (Fig. 2).

A pilot experiment (PP097) was performed at different temperatures and applied strain rates to explore the rheological behaviour of the sample over a wide range of conditions. Temperature was varied between 798-848 K and the shear strain rate was increased from 1•10 -5 to 1•10 -4 s -1 (Fig. 2; Table 2). A second experiment (PP098) was carried out at constant temperature (848 K) while performing three strain rate steps from 5•10 -5 to 3•10 -4 s -1 (Fig. 2, Table 2). The stress increased for increasing strain rate although the apparent viscosity (stress/strain rate ratio) decreased of about 7% as deformation rate increased. Experiment PP098 also showed some additional shear hardening (increase of stress with increasing strain) for strain larger than 0.5 (Fig. 2A). Inspection of this sample after deformation highlighted the presence of marked wrinkles on the metallic jacket (see inset in Fig. 2A), testifying for a marked strength difference between the sample and the iron jacket. The occurrence of wrinkles was responsible for the observed shear hardening. As a result, the possible influence of the metallic jacket on the rheological behaviour of sample PP098 deformed at 848 K precludes the possibility of interpreting the observed decrease of viscosity with increasing strain rate as an expression of non-Newtonian behaviour of the sample. Aiming to reduce the strength contrast between the sample and the metallic jacket, we performed the rest of experiments using copper jackets around the experimental assembly. In general, these two experiments gave similar apparent viscosities, which suggest sample homogeneity (Table 2). This supports the view that the relatively high viscosities measured at 848K in PP097 and PP098 were probably related to the use of an iron jacket, which gave less accurate rheological results because of higher strength of this metal with respect to the sample. Both the relatively small range of strain rates applied to the specimens and the significant variations of stress recorded during the experiments did not permit an accurate determination of the rheological behaviour of the material as function of applied strain rates. These experiments did, however, given indications on the rheological evolution of bubble-bearing melts with increasing deformation.

(FIGURES 3 AND 4) X-ray tomography and bubble analysis

Analyses of the 3D volumes reconstructed by X-ray tomography evidenced a number of changes associated with the deformation of bubble-bearing samples.

Increasing applied strain resulted in a change of bubble shapes from spherical to ellipsoidal and finally planar at γ of 9.6 (Figs. 3 and4).

Figure 3 displays the volume reconstruction for a sample that did not experience deformation (i.e. the starting material, A) and a sample in which total applied strain was 1.6 (B). Volumes for each bubble were measured by Blob3D software and the resulting vesicle size distributions are presented in Figure 5. Vesicle sizes correspond to the equivalent radius (radius of a sphere with the same volume as the object under consideration), and 4 stages of deformation are shown: γ 0, 1.6, 5.5, and 9.6. Data for γ 5.5 were obtained by analysing an additional section of experiment PP117 closer to the core where the applied strain is lower [START_REF] Paterson | Rock deformation tests to large shear strains in torsion[END_REF].

(FIGURE 5)

The 3D analyses indicate that deformation produced a general increase of bubble flattening (Figs. 3,4). Figure 5 shows the appearance of a population of larger bubbles already at γ 1.6. Increasing γ to 5.5 results in the generation of a large population of bubbles with relatively small volume, most likely associated with bubble breakage during deformation. At the highest strain the presence of bubbles with large equivalent radius (i.e. large volume) suggest strain induced bubble coalescence. This is in agreement with the observation of Okumura and co-authors (2008), which suggested that deformation promotes bubble coalescence.

The total volume of bubbles decreases only slightly with deformation (from about 2 to 1.5 vol.% at the highest total γ).

(FIGURE 6)

Water content analyses FTIR analyses were performed on the glass before and after deformation from the inner to the outer portions of the samples. The initial water content and water content at strain = 1.6 are the same within error; however, the water content at strain = 9.6 is significantly lower, at 0.2 wt.% (Fig. 6). Analyses of water content in a static experiment (PP144), performed with the same experimental setup and duration as PP117, gave the same water content as the starting material, suggesting that deformation was responsible for the loss of water.

Discussion

Experimental results provided information on the effect of bubble deformation on the viscosity of bubbly magmas and also on the influence of deformation on degassing.

(FIGURE 7)

Rheology and strain localization

Viscosities measured for the bubble bearing melts were compared with those of a bubble-free melt with the same composition [START_REF] Giordano | Viscosity of magmatic liquids: A model[END_REF]Fig. 7).

Results indicate that the measured viscosity at the lowest temperature and strain rate of 3•10 -5 s -1 is close to that of the bubble-free system (Fig. 7). On the contrary, at the highest temperature (848 K) the measured viscosities are always higher than those of the bubble free melt. This is likely related to the high resistance to deformation of the iron jacket used in the experiments, which masked the rheological properties of the sample.

The experiments performed at 823K with copper jacket are characterized by large oscillations of stress and the temperature recorded by the thermocouple with increasing strain (Fig. 2), with a minimum measured viscosity that is about one order of magnitude lower than the viscosity of the pure melt (Fig. 7). To quantify the influence of bubbles on the rheology of these samples, it is fundamental to characterize the behaviour of the gas bubbles during deformation. The bubble relaxation time (λ) is a measure of the timescale over which a bubble can respond to changes in its shear environment [START_REF] Llewellin | The rheology of a bubbly liquid[END_REF]:

λ = rη s Γ (1)
where r is the radius of the bubble, η s is the shear viscosity and Γ is the surface tension. For an average bubble radius of 9 μm (Figure 5), a surface tension between the gas and the melt of 0.25 Nm -1 [START_REF] Llewellin | Bubble suspension rheology and implications for conduit flow[END_REF] and melt viscosity at 823 K of 10 10.7 Pa•s; [START_REF] Giordano | Viscosity of magmatic liquids: A model[END_REF], λ is higher than 500 hours. In our experiments, the deformation times are much shorter than the relaxation time. The effect of surface tension between gas and bubble is thus negligible and the bubbles behave as passive tracer of shear (i.e. increasing deformation in simple shear induces flattening). Under such conditions, the viscosity of the diluted bubble-bearing melt can be calculated by effective medium theory [START_REF] Hashin | A Variational Approach to Theory of Effective Magnetic Permeability of Multiphase Materials[END_REF][START_REF] Manga | Viscosity of magmas containing highly deformable bubbles[END_REF][START_REF] Costa | A model for the rheology of particlebearing suspensions and partially molten rocks[END_REF], and the viscosity of the system is fundamentally controlled by the arrangement of the bubbles in the melt. If the bubbles are isolated and do not interact, and the viscosity of the gas (η g ) is approximated to zero (η g =6•10 -5 Pa•s at 823 K and 100 MPa; IAPWS, 1997), the viscosity of the system as function of the gas fraction is given by (η HS+ ; Hashin and Shtrikman upper bound; [START_REF] Costa | A model for the rheology of particlebearing suspensions and partially molten rocks[END_REF][START_REF] Manga | Viscosity of magmas containing highly deformable bubbles[END_REF][START_REF] Hashin | A Variational Approach to Theory of Effective Magnetic Permeability of Multiphase Materials[END_REF]:

η HS+ = η m 1- 5φ 3+ 2φ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ (2)
where η m is the melt viscosity (from Giordano et al., 2008), and φ g is the volume fraction of bubbles (Fig. 7). Figure 7 shows that the minimum viscosity measured during the experiments is much lower than expected for a material containing 2 vol.% of isolated bubbles (Eq. 2). An additional deformation mechanism is therefore required to account for such a difference. With increasing strain, bubbles did not simply become more elongated but also extremely flattened and their volume increased (Figs. 345). Strain-induced coalescence is most likely responsible for the increase of the volume of the bubbles. The combination of such coalescence with the extremely flattened shape of the bubbles results in the generation of planar, gas-rich structures in the sample. Small local variations of bubble fraction could result in strain localization in portions of the sample where the bubble content is higher. Since strain localization favours additional coalescence, the resulting pattern quickly becomes extended planar structures where additional localization occurs. The presence of such gas-rich planes where the strain localises could induce a substantial decrease of the bulk viscosity of the sample and account for the relatively low viscosity observed in our experiments.

The effect of such localisation could be even stronger since the calculations presented in Figure 7 do not take into account water loss from the melt and the related increase of viscosity induced by degassing. The loss of about 1.4 wt.% water (experiment PP117), at constant temperature of 823 K, would result in a 5 orders of magnitude increase of melt viscosity [START_REF] Giordano | Viscosity of magmatic liquids: A model[END_REF]. This would imply a significant contribution of strain localization to the bulk viscosity of the samples.

(FIGURE 8)

During deformation experiments, the measured viscosity varied continuously (Fig. 2B), reflecting variations in the volumetric fraction of sample affected by shear localization. An inverse correlation was present between these oscillations in viscosity and the increase of temperature recorded by the thermocouple (Figs. 2 C, D). A possible explanation for this occurrence is that coalescence and shear localization may have culminated in the formation of a gas network connected to the thermocouple hole pressurized at 0.1 MPa (Fig. 1B). In this respect, localization of strain on one or more gas layer/s could account for the minimum reached in the applied shear stress and the coincident maximum in temperature should reflect the passage of gas through the thermocouple hole (Figs. 2C, D and 8). This is consistent with the fact that at 100

MPa and temperature of 823K the gas (N 2 -O 2 -H 2 O; see starting material paragraph) is likely above the Joule inversion temperature and consequently an expansion produces heating of the gas phase (IAPWS, 1997).

To summarize, small local variations of bubble fraction are the likely cause of strain localization, which, in turn increases local strain and favours bubble coalescence. Under the unsteady flow conditions prevailing in our experiments, the vesicles tend to flatten with increasing deformation and generate low viscosity planar features on which the strain localises further. This positive feedback mechanism could be amplified by the local increase of temperature due to viscous heating [START_REF] Hess | Viscous heating in rhyolite: An in situ experimental determination[END_REF]. The positive feedback enhancing strain localization can only be ceased if a gas network is established and it connects to a lower pressure region. In this case, the gas is extracted and the bubble fraction decreases, causing a local increase of viscosity that could potentially lead to strain localization in another portion of the material.

Strain-induced degassing

The experiments demonstrate that deformation is responsible for the loss of gas from bubble-bearing melts. The deformation and coalescence of the vesicles with increasing applied strain may result in the generation of extended degassing paths, which increase the melt interface exposed to degassing. Additionally, the stretching of the bubbles associated to deformation reduces the thickness of the diffusive boundary layer increasing the concentration gradient present at the melt-gas interface, which in turn, increases the degassing flux into the connected bubble network (e.g. [START_REF] Lensky | Radial variations of melt viscosity around growing bubbles and gas overpressure in vesiculating magmas[END_REF]. This process increases the concentration gradient of the volatiles diffusing into the vesicles, accelerating the degassing process. The loss of water should induce a strong increase of the melt viscosity [START_REF] Giordano | Viscosity of magmatic liquids: A model[END_REF]. In our case, however, it was only slightly recorded (see the general increase of applied stress in Fig. 2B) in the experiment performed to a total strain of γ 9.6, because of the counteracting effect of shear localization on gas planes. The oscillations of stress and temperature recorded by the thermocouple suggest that degassing occurred cyclically (Fig. 2). The very low decrease of total bubble fraction with increasing deformation suggests, however, that residual bubbles remained in the melt once the connected bubble path sealed (Fig. 8).

This is in agreement with the fact that isolated, residual bubbles can only be closed once the gas present in the vesicles diffuses back to the melt [START_REF] Yoshimura | Diffusive dehydration and bubble resorption during open-system degassing of rhyolitic melts[END_REF]. The relatively low temperature and, consequently, the low diffusion rates of the gas phase in the melt (e.g. [START_REF] Zhang | Diffusion of Water in Rhyolitic Glasses[END_REF] strongly limits bubble resorption. Therefore, a scenario in which localization generates a connected gas network at different times and in different portions of the sample can reconcile rheological, FTIR and temperature data. This implies that, in our high pressure, isobaric experiments with a free surface intermittently connected to atmospheric pressure, degassing occurred in cycles and this process could eventually lead to a near complete degassing of magma. The extraction of gas from the melt phase is, in fact, a function of the final pressure at which the gas network is connected and the only limiting factor is the diffusion of the gas from the melt to the gas network.

(FIGURE 9)

Summary and implications

Experiments presented in this contribution corroborate the idea that deformation enhances bubble coalescence (e.g. [START_REF] Okumura | Evolution of bubble microstructure in sheared rhyolite: Formation of a channel-like bubble network[END_REF][START_REF] Okumura | Magma deformation may induce non-explosive volcanism via degassing through bubble networks[END_REF]. The results also show that the residual water content of a deforming magma is not necessarily function of the confining pressure, but it could reflect the pressure at which an eventual gas network was connected (0.1 MPa in our experiments).

Our experiments show also that deformation in unsteady conditions produces flattening of bubbles, which, combined with coalescence, could generate gas-enriched planar structures controlling the rheological behaviour of magma. Deformation in unsteady conditions is likely to occur in highly viscosity magmas (for a magma with viscosity 10 9 Pa•s, vesicles of 100 microns radius and surface tension of 0.25Nm -1 the bubble relaxation time is about 110 hours) and could play a role in the generation of banding often observed in obsidians (e.g. [START_REF] Castro | Vesiculation rates of obsidian domes inferred from H2O concentration profiles[END_REF][START_REF] Gonnerman | Flow banding in obsidians: A record of evolving textural heterogeneity during magma deformation[END_REF].

During ascent in a volcanic conduit, the release of gas from magma can occur via three main processes: 1) the formation of extended gas networks connected to lower pressure (shallower depths in the volcanic conduit), 2) the transition from viscous to brittle flow of magma, which would result in the generation of cracks with reduced pressure attracting the gas-phase (i.e. [START_REF] Tuffen | Repeated fracture and healing of silicic magma generate flow banding and earthquakes?[END_REF][START_REF] Tuffen | Fault textures in volcanic conduits: evidence for seismic trigger mechanisms during silicic eruptions[END_REF], or 3) cracking of the volcanic conduit. The first process requires a significant length scale for the connected bubble network and evaluating its importance is not a trivial task. On the contrary, a plethora of field evidence exists for the second process [START_REF] Tuffen | Repeated fracture and healing of silicic magma generate flow banding and earthquakes?[END_REF][START_REF] Tuffen | Fault textures in volcanic conduits: evidence for seismic trigger mechanisms during silicic eruptions[END_REF]. The third process has been documented by field observations of magmatic vents [START_REF] Stasiuk | Degassing during magma ascent in the Mule Creek vent (USA)[END_REF], though shear stresses generated during magmatic flow along the conduit wall are not high enough to induce failure of the wall rocks (shear stress lower than 1 MPa for reasonable viscosity of the magma and dimension of the conduit; [START_REF] Stasiuk | Degassing during magma ascent in the Mule Creek vent (USA)[END_REF][START_REF] Thomas | Volcanic rock-mass properties from Snowdonia and Tenerife: implications for volcano edifice strength[END_REF]. Nevertheless, along the conduit wall, where the strain suffered by magma is the largest, deformation could result in the generation of a connected gas network (Fig. 9B; e.g. [START_REF] Llewellin | Bubble suspension rheology and implications for conduit flow[END_REF]. If the pressure of the gas is higher than the confining pressure because of viscous retardation of bubble growth, which is typical for high viscosity magmas (Viscosity>10 9 Pa•s; [START_REF] Gonnerman | The fluid mechanics inside a volcano[END_REF], the pore pressure in the wall rock would increase, decreasing the effective stress and eventually triggering extensional fracturing of the wall rocks [START_REF] Terzaghi | Stress conditions for the failure of saturated concrete and rock[END_REF]Fig. 9). This mechanism could be a complementary process producing hybrid earthquakes during volcanic eruption (e.g. [START_REF] Tuffen | Repeated fracture and healing of silicic magma generate flow banding and earthquakes?[END_REF].

An additional implication of the experimental results presented in this study regards the genesis of obsidians. Obsidians are generally depleted in water (Gottsmann andDingwell, 2001, 2002;[START_REF] Rust | Determining flow type, shear rate and shear stress in magmas from bubble shapes and orientations[END_REF][START_REF] Castro | Vesiculation rates of obsidian domes inferred from H2O concentration profiles[END_REF] and contain very limited amount of crystals [START_REF] Castro | Dynamics of obsidian flows inferred from microstructures: insights from microlite preferred orientations[END_REF][START_REF] Castro | Microlite textures and volatile contents of obsidian from the Inyo volcanic chain, California[END_REF]. The possibility of continuous H 2 O-degassing already at depth (i.e. from magmas with low bubble content) would reduce the amount of nucleation and growth of crystals [START_REF] Hammer | Experimental Studies of the Kinetics and Energetics of Magma Crystallization[END_REF] during magma ascent. Additionally degassing will result in a substantial increase of viscosity, which would further inhibit crystallization [START_REF] Dingwell | The Fluxing Effect of Fluorine at Magmatic Temperatures (600-800-Degrees-C) -a Scanning Calorimetric Study[END_REF][START_REF] Dingwell | The glass transition in hydrous granitic melts[END_REF]. In conclusion strain-induced degassing could result in water under-saturation already in the early stages of magma ascent, reduce the tendency of the magma to crystallise and finally bring to the eruption of water and crystal poor magma, i.e. obsidians.

Figure Captions

Figure 1: Sketch of the experimental assembly used for the experiment. (B)

Illustration of the possible path for gas-escape from the samples. The inset shows how gamma (γ) is calculated [START_REF] Paterson | Rock deformation tests to large shear strains in torsion[END_REF].

100

  MPa confining pressure and copper jacketExperiments PP116 and PP117 were performed at constant temperature (823 K) and at the lower confining pressure of 100 MPa. No wrinkles on the metallic jacket were observed with this new experimental configuration. Large stress instabilities (up to about 4 MPa) were observed in both experiments and were associated with significant variations in the temperature (up to 6 K) recorded by the thermocouple atop the specimens (Fig.2 C and D). A closer investigation of the relationship between stress and temperature instabilities revealed that the oscillation of stress and temperature were out of phase by about 90° (i.e. a minimum in stress corresponded to a peak in temperature; Fig.2 C and D).

Figure 2 :

 2 Figure 2: (A-B) Variation of the applied shear stress as function of shear-strain. The maximum shear strain is γ =1.6 and γ =9.6 for (A) and (B) respectively. The picture in figure (A) is from the external portion of the experiment PP098 performed to a total γ

Figure 3 :

 3 Figure 3: X-ray tomographic images of the starting material (A) and experiments PP116 deformed to γ 1.6 (B). The sketch of the sample in the inset shows the

Figure 4 :

 4 Figure 4: (A) 3D reconstructions of an internal section of the experiment PP117. This volume of sample underwent a deformation corresponding to γ 5.5 (Paterson and

Figure 5 :

 5 Figure 5: Frequency distribution of bubble volumes expressed as equivalent radius

Figure 6 :

 6 Figure 6: Water content measured by FTIR for the starting material, a series of

Figure 7 :

 7 Figure 7: Logarithmic value of the apparent viscosity measured during the

Figure 8 :

 8 Figure 8: Values of recorded stress during the experiment PP116 against strain. The

Figure 9 :

 9 Figure 9: Possible evolution of the stress applied to the wall conduit during magma

Acknowledgements

This project was financed by an INSU grant and the Electrovolc project, which is funded by the French national agency for research (ANR): contract JC05-42707 to Fabrice Gaillard and by the NERC grant (NE/G012946/1) to Luca Caricchi.

We are grateful to the local contacts Peter Modregger and Federica Marone at Swiss Light Source to make possible the x-ray tomography experiments and for their help with the 3D reconstructions and data treatment. The scientific discussions with Fabrice Gaillard, Remi Champallier, Alison Rust and the technical support of Philip Teulat were greatly appreciated. The comments of Satoshi Okumura and two anonymous reviewers greatly improved the manuscript.

Cu jacket