Ivan Sánchez

Oleg Davidyuk

Jukka Riekki

Towards User-Oriented Application Composition

Keywords: Ubiquitous application composition, service composition, physical user interface, allocation algorithm;

This paper presents an autonomic system for composing ubiquitous applications at run-time. The applications are composed according to the user preferences collected via a physical user interface. This interface allows users to specify preferences by simple actions of touching with their mobile terminals icons in the environment, instead of explicitly selecting resources and dealing with their properties. In this paper, we present a system prototype and an example multimedia application. We also evaluate the performance of the prototype and the allocation algorithm which is used to compose applications.

I. INTRODUCTION

Application composition is a concept that emphasizes building applications from a number of components which are physically allocated on multiple computational devices available in a ubiquitous smart space. This concept increases the flexibility of application adaptation and also enables a number of useful scenarios.

In addition to ubiquitous applications, the potential scenarios of application composition include virtual devices, multimodal interfaces, and load distribution [START_REF] Buford | Composition trust bindings in pervasive computing service composition[END_REF]. The virtual device approach (also known as resource sharing) assumes that aggregating functionality across many resource-limited devices increases the capacity of each single device used in the aggregation. E.g., a portable video camera connected to a mobile phone enables the mobile phone to access data stored in the camera's memory and to send video messages. Application composition can also be used to achieve load distribution among personal devices by decomposing applications and allocating their heavy-weight components onto the nodes with the required computational capacities. This functionality is required, among others, in such domains as content-based retrieval, information fusion, and semantic search. In addition, application composition enables the construction of multimodal user interfaces by combining and controlling inputs and outputs from various ubiquitous devices.

Recently, application composition has become an important domain also for autonomic systems. Such systems require the users to specify a desired application only, which is then realized as needed in an autonomous manner. However, this functionality requires that the autonomic system is capable of discovering resources, comparing resource properties and, selection of an optimal application allocation (i.e. a combination of resources and application components). Besides, such an autonomic system has to be able to adapt composed applications when the context or the user goals change. Depending on the available resources, even the same application can be appropriately realized using different resource combinations. Autonomic systems are essential in smart spaces offering a great amount of services and devices, because users may become too overloaded with manual controlling and configuring applications, and thus, they may even stop using them.

Several systems for automatic application composition have been proposed. For example, Sousa et al. [START_REF] Sousa | Task-based adaptation for ubiquitous computing[END_REF] presented a system for self-adaptation of composite applications on several architectural levels. Their approach is to specify the applications as abstract tasks, which are subject to the QoS requirements defined by the end-users. Sousa's framework calculates the optimal resource allocation and reallocation for each task using a Knapsack problem solver. Sousa's research also focuses on expressing application requirements using a set of user interfaces for collecting requirements which are then forwarded to the problem solver. In their most recent work [START_REF] Sousa | udesign: End-user design applied to monitoring and control applications for smart spaces[END_REF], these authors presented an architectural style called uDesign, which focuses on applying end-user programming techniques to the assembly of personalized applications used for monitoring and controlling smartspaces.

Another example of an application composition system is the COCOA middleware [START_REF] Mokhtar | Cocoa: Conversation-based service composition in pervasive computing environments with qos support[END_REF]. This middleware supports the composition of task-based applications which are modeled using workflows and QoS properties. The COCOA middleware is based on a service discovery mechanism that can handle semantic heterogeneity; in addition, it utilizes an ontology-based matching algorithm with QoS support for application composition.

Similar solution, the Galaxy [START_REF] Nakazawa | Galaxy: a service shaping approach for addressing the hidden service problem[END_REF] framework, focuses on the interoperability of devices in ubiquitous environments. Galaxy supports composite services which control and cooperate with ubiquitous devices. Galaxy, as well as COCOA, targets semantic-free service composition issues. The Pervasive Component System (PCOM) [START_REF] Handte | Supporting pluggable configuration algorithms in pcom[END_REF] offers an infrastructure for multiple application composition algorithms as certain application scenarios may require changing the algorithm at runtime.

All aforementioned solutions target allocation of only one application component at a time, while our approach deals with multi-component allocation and optimization of the structure of the whole application according to context and user needs.

In this paper, we present a prototype of an application composition system, an example application, and results from the performance tests. In our prototype, application composition is carried out in two phases. In the first phase, a user specifies her/his preferences by simply touching icons attached to physical resources in the environment. The user touches the icons using a mobile phone, hence the phone is used as a physical tool to interact with the environment (i.e. the phone is the part of a physical user interface). In the second phase, the allocation algorithm [START_REF] Davidyuk | Algorithms for composing pervasive applications[END_REF] composes an application fulfilling the requirements set for the application (including the requirement to use the resources selected by the user). The REACHeS framework [START_REF] Sánchez | Controlling multimedia players using nfc enabled mobile phones[END_REF] is used to integrate the physical user interface, the allocation algorithm, and the rest of the required components into the complete system. We also conducted a user evaluation to study the feasibility of our system. The results of the user evaluation are presented in [START_REF] Davidyuk | Autonomic composition of ubiquitous multimedia applications in reaches[END_REF].

II. THE APPLICATION COMPOSITION CONCEPT

The application composition concept assumes that applications are built from a set of components which may reside on physically distributed nodes. Figure 1 shows the key components of our system. The Context Management component handles the user context and triggers the application adaptation when needed. The Application Assembly controls the application's lifecycle and also performs the application adaptation by composition. The Resource Management monitors the utilization of resources and performs application deployment. The Service Discovery handles information about nodes available in the environment and provides the matchmaking functionality. The applications are started and then the composition process takes place in three phases as follows:

The first phase. This phase of the application composition process is started either explicitly, when the user activates the application, or implicitly, after the Context Management component triggers composition. In the former case the composition is triggered by the user through a physical user interface. That is, the user requests the composition by touching with her/his mobile terminal a corresponding icon in the environment. Then, the Application Assembly searches for the available local nodes (that is, nodes in the user's close proximity, e.g. in the same room), or remote nodes (that is, nodes located physically far away from the user) through the Service Discovery. Conventional protocols, such as Bluetooth or UPnP, can be used. Application Assembly searches the nodes according to their functional and non-functional (i.e. resource) properties. The functional properties of a node denote its ability to provide certain services. Functional properties are descriptions and resemble interface statements in Java. They can also rely on ontologies to enable semantic search, as suggested by Mokhtar et al. [START_REF] Mokhtar | Cocoa: Conversation-based service composition in pervasive computing environments with qos support[END_REF]. Functional properties can be also used to indicate the availability of specific resource (e.g. a file or a user profile) at a certain node. The non-functional properties, in their turn, mainly denote device resource constraints, such as the maximum available memory or the computational resource capacity. Furthermore, these properties may be used to implement user access policies.

The second phase. We assume that a node can host one or more application components as long as the node's resource capacities are not exceeded. Besides, the functional properties of nodes and components have to be met. These two conditions are ensured during the second phase of the application composition process which is performed by the Application Assembly. This phase is the most important step in the application's startup and the execution stages. The goal of the phase is to produce a valid application composition. If no valid composition is found, the service discovery (i.e. the first phase) and the application allocation (i.e. the second phase) are iteratively repeated. It is possible that some applications might not be allocated due to their high resource demands or specific functional constraints which cannot be met by the nodes in the environment. In such cases, the Application Assembly may use another application profile with lower resource demands or downsize the resource demands through interaction with the user.

The third phase. After the valid application composi-tion is found, it is then realized by leasing the necessary computational resources, deploying the components onto them and configuring the application. This can be achieved using a resource management schema, as suggested in [START_REF] Jurmu | Screenspot: Multidimensional resource discovery for distributed applications in smart spaces[END_REF]. However, the resource management is out of scope of this paper.

A. The Application Allocation Algorithm

Our approach focuses on optimizing the application compositions according to user preferences. An optimal application composition can minimize bandwidth consumption, balance load among the nodes, and meet the various resource requirements imposed by the application components. As the optimization goals and resource availability may vary during the application execution, they sometimes affect application compositions built earlier, making them invalid or no longer optimal. In these cases, a reallocation of the application is performed.

Finding an optimal application composition which satisfies the numerous functional and resource requirements is a complex problem and solving it requires the utilization of an allocation algorithm. Such an algorithm can be used to find an appropriate application composition which satisfies the node constraints after the application components are assigned to the chosen nodes. In other words, the algorithm solves the application allocation problem.

Our application allocation algorithm [START_REF] Davidyuk | Algorithms for composing pervasive applications[END_REF] is part of the Application Assembly component in Figure 1. This algorithm operates with two models, an application and a platform model. The application model defines the structure and the properties (e.g. application resource requirements) of the application. The platform model, in its turn, formally defines the network resources and their properties (e.g. node resource constraints). Both models are represented in the form of graphs, where nodes represent application components or network nodes and links model communication links (between application components or network nodes). Each element of the models can have multiple properties which specify non-functional requirements like computational resources, up or downlink channel capacities, and memory demand. Each property can be expressed by a float, an integer, or a Boolean value. The values of application properties may be set by measuring the performance of the application under different workloads and recording this data onto application resource profiles. The values of platform model properties may be measured using various resource and network monitoring tools. The task of capturing the resource requirement values is essential for the correct functioning of the allocation algorithm, but is out of the scope of our paper.

Our application allocation algorithm supports special kind of user preferences, which we call affinity constrains. These constraints restrict the deployment of an application component by specifying a set of permitted nodes for that component. These constraints have multiple purposes. For example, they can be used to represent the user trust preferences, similar to the Component Trust Binding prototype [START_REF] Buford | Composition trust bindings in pervasive computing service composition[END_REF]. Thus, the user can specify a set of trusted nodes for each application component, and then, the algorithm will allocate the components onto the trusted nodes only. These affinity constraints enable the so-called 'visibility', a notion introduced by Malek et al. [START_REF] Malek | A decentralized redeployment algorithm for improving the availability of distributed systems[END_REF], which means that each network node has a 'domain' or a set of all the nodes it is aware of. The visibility is an important feature for ubiquitous environments where the handling of handoffs is necessary in the application layer (e.g. in wireless networks). Besides, the affinity constraints enable reliable application composition like in the prototype developed by Del Prete et al. [START_REF] Prete | Reliable discovery and selection of composite services in mobile environments[END_REF].

To achieve this, our platform model has to have additional properties specifying reliability of each network node. The allocation algorithm will then maximize the reliability of the whole composed application. The affinity constraints are also helpful if an application component requires access to some specific resource (e.g. a file) that is only available at a certain node. In our prototype, the user creates the affinity constraints by touching with the mobile phone the physical resources that he would like to use with the application.

In order to solve the application allocation problem at runtime, the Application Assembly uses a genetic algorithm that relies on mutation and crossover operators and iteratively evolves multiple solutions. The algorithm optimizes a generic objective function that supports multiple objectives without redesigning the algorithm's code. The algorithm also supports generic application and platform models which can be easily modified to add and remove additional properties, thus the number of properties used in our models is not fixed.

B. The REACHES Framework

We realized the application composition concept using the REACHES framework [START_REF] Sánchez | Controlling multimedia players using nfc enabled mobile phones[END_REF] which enables the utilization of a mobile terminal's UI to control a wide range of ubiquitous applications. These applications can be composed dynamically from service components which process asynchronous events generated by users. The REACHES clients are resource-restricted mobile terminals, thus, all computationally-heavy tasks (including the generation of UIs and the application allocation) are performed on the REACHES server. The REACHES architecture (presented in Figure 2) is centralized and consists of four components: Remote Control, User Interface Gateway, System Display Control, and Service Components.

The Remote Control consists of a physical UI (a set of RFID tags) placed in the user's local environment and of a mobile terminal equipped with an RFID reader. The RFID tags contain commands which are triggered when the tags are read using the terminal. We use these tags in our prototype in order to trigger an application to start, utilize The User Interface Gateway (UIG) connects users and service components. Its main purpose is to synchronize different subsystems by processing events from the Remote Control and dispatching them to appropriate service components. In addition, the User Interface Gateway performs the service discovery functions: it registers and unregisters services, establishes connections between them, and provides the matchmaking functionality.

The System Display Control (SDC) is intended for multimedia applications. It connects external resources (e.g. displays) to the REACHES server. After the UIG registers a resource, the browser, which is hosted on a computer connected to the resource, loads scripts (REACHES client) that enable communication between the SDC and the browser. The REACHES architecture does not require deploying any other software on the resource side.

When an application is started, the system assigns one or more services and resources to it. Then, the service components send events to the resource via the SDC, which dispatches each event to the corresponding browser to perform the requested update to the user interface.

The Service Components perform application specific functions and are allocated onto remote computation nodes. The Service Components communicate with the other elements of the REACHES architecture via the UIG.

The REACHES framework implements most of the functionality shown in Figure 1. The user provides his/her preferences and triggers the application composition by touching icons in the environment (corresponds to the Context Management). The Application Assembly is performed by the allocation algorithms executed by the UIG. The UIG is aware of all resources and services available for certain context (corresponds to the Service Discovery). The SDC deploys application onto the resources (corresponds to the Resource Management).

C. The Ubiquitous Multimedia Player Application

We integrated a multimedia player application into the REACHES to demonstrate features of the framework. The application is based on Flash and supports various content including audio, video, images and flash multimedia files. The player allows rendering of multimedia files, supports streaming, and accepts dynamic playlists.

The application controller UI is shown in Figure 3 (A). The users controls the player using the mobile phone's UI as follows. The Service Component (SC) manages the multimedia content. and receives commands (generated by the user) from the Remote Control. These commands are interpreted and dispatched to the external display which embeds the multimedia player and executes the commands with the action required. The URL specifying details of the playlist file can be stored as a parameter in a RFID tag. This data is delivered to the SC when the application is started. The RFID-based control panel for the application is shown in Figure 3 (B).

III. EXPERIMENTAL EVALUATION

We used the REACHES application framework to create a prototype of a system for application composition. Firstly, we embedded the application allocation algorithm in the framework and, tested the performance of our allocation algorithm on synthesized datasets. Our aim was to use the algorithm for real-time application composition; therefore, the computational load has to be low even when handling large application and platform models. We also tested whether the algorithm was executed correctly. The introduction of the affinity constraints made this point even more interesting. Secondly, we measured the multimedia application startup latency caused by the REACHES framework. Here, our goal was to analyze factors contributing to latency while increasing the number of the real ubiquitous resources in an environment.

The allocation algorithm was implemented in C++ and tested using the Boston University Representative Internet Topology Generator (BRITE) tool [START_REF] Brite | The boston university representative internet topology generator[END_REF]. The application and the platform models contains six different QoS properties, the values of which are randomly generated. We also included affinity constraints in these models as follows: each application node α from the application model A was associated with a set of nodes S from the platform model P. Nodes from the set S i ⊂ P were permitted to host the component α i . However, the affinity constraint of each platform node β / ∈ S i did not permit β to host the application α i even if β satisfied all the other constraints. Elements of these sets S i ⊂ P were chosen randomly, and cardinality of S i was set to 90 per cent of cardinality of S.

We performed the experiments under Red Hat Linux 4.1.2, on an AMD Opteron dual core 270 [2GHz] PC with 8 GB memory, but only one processor core was used to execute the algorithms. Figure 4 (plotted on a logarithmic scale) shows how the performance of the allocation algorithm with the affinity constraints present (curve A) and the original algorithm (curve B) is affected by the cardinality of the models.

The figure shows that the cardinality of the platform model was gradually increased from 30 to 255 nodes, by 5 nodes in each subsequent iteration in of the experiment. The platform model's cardinality was always computed as |P| = |A| • 3, where A and P correspond to application and platform models.

The reported measurements were recorded over 100 runs. The resulting curves (see Figure 4) show that the latency of the algorithm depends on the application (and the network) complexity. However, the presence of affinity constraints had an insignificant impact on the performance of the algorithm, which can be explained by the fact that affinity constraints actually reduce the search space, i.e. the algorithm goes through fewer solutions.

Although the latency is high for the large application sizes (e.g. 200 components), this is not a severe problem, as it is reasonable to assume that the real-world application sizes will not exceed 30 components, based on the current application estimates. As the test revealed, the algorithm spent only 12 milliseconds to process this scenario. Thus, we found the performance of our algorithm suitable for realtime tasks: we believe that the latency of the algorithm will be dwarfed by the latencies introduced, for example, by the service discovery process.

Next, we evaluated the performance of the whole system. The goal of the experiment was to study the performance of the REACHES server and also to identify possible bottlenecks. We implemented the REACHES using Java servlets which were ran in Tomcat 5.5. The mobile terminals used were Nokia 6131 NFC phones, equipped with RFID (NFC compliant) readers. The application in the mobile terminal controlled the remote network resources using a J2ME MIDlet client.

The network resources consisted of PCs connected to the REACHES server. Each PC ran the REACHES client, which executes server requests locally. The clients communicated with the server using the HTTP protocol. The allocation algorithm was integrated into the REACHES server to start and adapt the applications. We measured the latencies of the REACHES server as follows:

• Service Discovery latency is the time delay spent for acquiring available resource descriptions from the local database.

• Algorithm Execution latency is recorded from the moment when the server starts the algorithm execution until the algorithm returns an optimal solution. This latency also includes the time overhead used to create application and platform model files and the time delay spent to associate the found solutions with the resources in the database. • Other processes latency includes the request processing time delays caused by the server and the communication latencies between resources and the server. • Overall latency includes all the aforementioned overheads and is measured as the time interval from the moment the server received a request from the user to start an application until the resources are acquired and the application is started. However, we omitted the communication latency between the application client in the mobile terminal and the server because its values fluctuated a lot. This was due to high variability in the quality of the GPRS connection during the test. The latencies were measured during the presence of an increasing number of ubiquitous network resources. Figure 5 summarizes the experimental results. Each latency value was recorded in over 30 measurements.

As the graphs show (Figure 5), the Algorithm Execution latency occupies approximately 85 per cent of the Overall latency, thus dominating the other processes. The Service Discovery latency, which has the second largest values, occupies from 5 to 19 per cent of the Overall latency.

It should be noted, that in this test, the Algorithm Execution latency also included the time delay spent for parsing the data received from the server and transforming this data into the format understood by the algorithm. On the other hand, we left this delay out when we tested the algorithm as a stand-alone tool earlie (see Figure 4). Moreover, in the second test, an additional delay was caused by the fact that the REACHES, which was implemented in Java, used a separate C++ process to access the running algorithm.

Also, we noticed that the Service Discovery latency was slightly longer when a larger number of network resources were present in the environment. Although the service discovery performance was acceptable in this experiment, we believe that it may cause bottlenecks when, e.g., more than 100 resources are present. The Overall latency was 3 seconds when 30 resources were available in the environment, and this value is acceptable to the users as we revealed in the user experience tests with our prototype [START_REF] Davidyuk | Autonomic composition of ubiquitous multimedia applications in reaches[END_REF].

IV. CONCLUSIONS AND FUTURE WORK

The autonomic system for application composition presented in this paper is intended for everyday use in ubiquitous environments. Our system composes and adapts applications accordingly to user preferences and user-provided criteria. Thus, the system minimizes the users' cognitive load and increases usability of ubiquitous environments, as the users do not explicitly need to select resources and also deal with their properties. To address this, we designed an allocation algorithm which is capable of finding optimal application compositions in the real environment and for different applications. The problem of finding optimal application compositions belongs to the class of NPhard problems [START_REF] Kichkaylo | Constrained component deployment in wide-area networks using ai planning techniques[END_REF] and is exacerbated by the fact that the problem's search space does not contain information about the direction of the search, as we revealed in [START_REF] Davidyuk | Algorithms for composing pervasive applications[END_REF].

We tested performance of the allocation algorithm in two setups: (i) on synthesized datasets as a stand-alone tool, and (ii) with the real multimedia application when the algorithm was integrated as a part of the REACHES framework. The algorithm demonstrated performance which we found eligible for real-time application composition.

Our future work addresses several issues. At first, we are enhancing autonomy of the REACHES in order to incorporate additional context elements to fully support the user's mobility and traversing of application sessions in adjusting ubiquitous environments. We believe that the role of mobile resources is increasing, and applications are going to rely more and more on these resources in the future.

The second issue addresses the functionality of the algorithm which has to be extended in order to take into account mobile resources. This requires dealing with the realtime resource availability and also predicting the reliability of application compositions. For that reason, we need to include an additional component to the REACHES which is capable of estimating, according to existing behavioral patterns, for how long different resources in the environment stay available. Thus, the allocation algorithm will be able to evaluate different application compositions according to their reliability. The predictor can be designed, as suggested by Del Prete and Carpa [START_REF] Prete | Reliable discovery and selection of composite services in mobile environments[END_REF].

Figure 1 .

 1 Figure 1. The Application Composition Concept.

Figure 2 .

 2 Figure 2. The REACHES Framework's Architecture.

Figure 3 .

 3 Figure 3. The remote controller GUI (A) and the control panel for choosing the quality (B).

Figure 4 .

 4 Figure 4. The allocation algorithm performance test. The curve A denotes the case when affinity constraints were present and the curve B corresponds to the original algorithm (without affinity constraints).

Figure 5 .

 5 Figure 5. The REACHES Server Performance.

ACKNOWLEDGMENT

This work has been funded by Academy of Finland, Finnish Graduate School in Electronics, Telecommunications and Automations (GETA) and Nokia Foundation. The authors would like to thank Jon Imanol Duran for helping out with the testing and Jiehan Zhou for his valuable comments regarding the paper.


Status of the OPERA neutrino experiment H. Pessard on behalf of the OPERA Collaboration

The OPERA long-baseline neutrino oscillation experiment is located in the underground Gran Sasso laboratory in Italy. OPERA has been designed to give the first direct proof of   appearance, looking at the CNGS   beam 730 km away from its source at CERN. The apparatus consists of a large set of emulsion-lead targets combined with electronic detectors. First runs in 2007 and 2008 helped checking that detector and related emulsion facilities are fully operational and led to successful first analysis of collected data. This paper, after a short description of the OPERA setup and methods, gives an updated status report on data reconstruction and analysis applied to available samples of neutrino events

The CNGS program and OPERA

Following the discovery of oscillations with atmospheric neutrinos by Super-Kamiokande in 1998, accelerator neutrino projects developed in Japan and the USA to measure the   disappearance at long distance. The   disappearance signal is now confirmed by K2K and MINOS. In Europe, long baseline projects focused on the   appearance in a   beam. They led to the construction of the CNGS (CERN Neutrinos to Gran Sasso) beam at CERN, whose main physics objective is to prove explicitly the     nature of the atmospheric oscillation.

To achieve this purpose, the OPERA experiment, using targets made with lead and nuclear emulsions, was developed by an international collaboration of 12 countries and ~200 physicists to operate in the Gran Sasso underground laboratory, 730 km away from CERN. Construction started in 2003. The experimental setup was completed in 2008 and is now in operation.

The CNGS beam is a dedicated wide band neutrino beam, with a mean energy of 17 GeV optimized for   production and detection. New SPS beam extraction, target and focusing horns, km long decay tunnel have been constructed from 2000 to 2006. With a foreseen intensity of 4.5 10 19 400 GeV protons on target (p.o.t.) per year (assuming 200 days of operation), the number of neutrino interactions expected to occur in 1.25 kiloton of OPERA targets in 5 years is about 24000. The number of   CC interactions is then about 120 for m 2 = 2.5 10 -3 eV 2 , leading to the observation of about 10   CC events with less than one background event.

OPERA detector principles

The OPERA experiment is based on the direct observation of the  decay topology in nuclear emulsion films, the only technique providing micron level spatial resolution. Charged tracks produce ~32 grains /100 m of emulsion, allowing reconstruction accuracies of order 1 m in position and 1 mrad in angle. The detection of   CC events by the  decay kink and/or the impact parameter of the daughter in 1-prong  decay modes (84% total branching ratio), and by the displaced  vertex in the 3prong  decay mode (15%) is based on emulsion films for tracking, associated with high density plates as targets. This technique, used for the   discovery by DONUT in 2000, was brought to an industrial scale in OPERA (100 000 m 2 of films).

The necessity of keeping film alignment within micron precision while achieving a target mass of more than a kiloton led to design highly modular targets. The basic target unit is a brick of 10.2 x 12.8 x 7.9 cm made of 56 lead plates and 57 emulsion films. The emulsion films are made of a 205 m plastic base with two emulsion layers of 44 m, they alternate with 1 mm thick lead plates. Each brick (Fig. 1, left) has a removable pair of Changeable Sheets (CS) films on its downstream face. There are altogether 150 000 bricks for a total mass of 1.25 kiloton.

The OPERA detector [START_REF] Acquafredda | The OPERA experiment in the CERN to Gran Sasso neutrino beam[END_REF] is composed of two identical parts, each made of a target section and a muon spectrometer (Fig. 1, right), with an upstream large size RPC veto detector. In each target section, steel trays able to hold brick rows in vertical walls alternate with 31 planes of electronic detectors, the Target Trackers (TT) made of crossed 7 m long scintillator strips read at both ends via WLS fibers by 64-channel PMT. TT allow triggering on neutrino interactions and localizing the bricks in which they occured. Each muon spectrometer is composed of a large dipolar iron magnet instrumented with 22 RPC planes and complemented by 6 sections of drift tubes for precision tracking through the magnetic field. These detectors are used to identify muons emerging from the interactions and measure their momentum and charge, an important feature to distinguish background events containing   -produced charm particles. showing its structure and the CS films packaging. On the right, a picture of the OPERA detector shows the two target sections (black covers) and their spectrometers. One of the brick manipulators is seen operating along the second target block.

The OPERA event flow and analysis

The OPERA data acquisition is synchronized with the CNGS beam by a double GPS system with an accuracy of 100 ns, leaving negligible cosmic background among on-time events. After event track reconstruction in the TT and spectrometer detectors, interactions occurring in target areas are selected and the probability to contain the neutrino interaction vertex is computed for surrounding bricks. Highest probability bricks designated by the brick finding algorithm are extracted continuously by the Brick Manipulator System (BMS) and exposed to frontal X-rays to create alignment references between CS and brick films.

CS films are detached and analysed to validate the brick selection and provide predictions for the event localization. If a TT-predicted track is found in the CS, the brick is exposed to lateral X-rays, then to high energy cosmic rays in the surface laboratory, to generate alignment tracks. The brick is then unpacked, its emulsion films are developed and sent to the scanning laboratories of the Collaboration for vertex location and further data collection in the emulsions relevant for decay searches. If no matching track is found in the CS, the brick is returned to the detector with new CS and the next brick in the probability list is extracted.

Automated emulsion scanning of CS and brick films is shared between Europe and Japan. CS scanning is centralized in two laboratories, at Gran Sasso (LNGS) and at Nagoya University. Scanning is done with computer driven microscopes. CMOS cameras and commercial hardware are used with software algorithms in the microscope system common to the nine European scanning labs. Fewer but faster (up to 75 cm 2 /h compared to 20 cm 2 /h) systems using high-speed CCD cameras with custom mechanics and hard-coded algorithms are exploited in Japan.

Tracks found in the CS are searched for in the most downstream film of the brick and followed back in the preceding films. Track stopping indicates a possible vertex. To confirm and study a vertex, an area of about 1 cm 2 is measured in 5 films upstream and 5 films downstream. All tracks found in this volume are input to a vertex reconstruction program tuned to find decay topologies. To complete the kinematical analysis of the event, a momentum measurement algorithm using Multiple Coulomb Scattering in the lead plates is applied for low energy tracks. In addition, electromagnetic showers developing in the plates can be measured, their direction and energy reconstructed, and electrons identified.

OPERA running and first results

The OPERA electronic detector construction was completed in spring 2007. After a research period devoted to brick packaging and lead-emulsion compatibility studies, 150 000 bricks have been assembled from March 2007 to June 2008 by an automated Brick Assembly Machine located in the underground laboratory. Produced at an average rate of 700 per day, bricks have been continuously inserted into the detector by the BMS during the same period.

After a short commissioning run in 2006 without bricks, the CNGS operation started in September 2007 with 40% of the OPERA bricks. Due to radiation shielding problems in the CNGS target zone, this run lasted also just a few days, 38 interactions were recorded in the bricks for 0.08 10 19 protons delivered on target. The first runs allowed checking the beam time synchronization [START_REF] Acquafredda | First events from the CNGS neutrino beam detected in the OPERA experiment[END_REF] and the reconstruction of CNGS events with the electronic detectors.

A first long OPERA physics run took place from June to November 2008, although poor performance in the first three months limited the average efficiency of the CNGS to about 60%. OPERA recorded 10100 events and among them ~1700 interactions in the targets for 1.78 10 19 p.o.t. delivered. All subdetectors were operational and the live time of the data acquisition system was ~99%. Brick extraction, handling of bricks and CS, CS development and scanning, brick dismounting, film development and shipping, film scanning, all large engineering tasks, were validated at nominal speed during the 2008 run. Following improvements in reconstruction and analysis procedures [START_REF] Agafonova | The detection of neutrino interactions in the emulsion/lead target of the OPERA experiment[END_REF], successive steps of the data collection from the bricks developed in a progressive manner, as illustrated by the brick processing statistics (Figure 2). At the time of the conference, 797 interactions vertices had been located (119 '0-' and 678 '1-' interactions), allowing to start decay searches.

The CS principle worked as expected to perform efficient track matching between TT and brick emulsion films. Brick finding rate after the 2 nd brick is presently ~80%. Work in progress to improve brick prediction algorithms will benefit from the publication on database of larger statistics. Investigation of background and efficiencies from the data will also become possible.

The decay search is ongoing in the 2008 sample and a number of interesting events have already been found, namely charm decay candidates. Charm events, with topologies similar to  events, are crucial to cross-check  identification efficiency. Figure 3 shows a charm candidate as seen in the emulsions and illustrates important progress achieved in the last months to identify short distance decays, by recovering tracks found in only one of the two emulsion layers of the film. The method improves also significantly the track impact parameter distribution in vertices, as shown in Figure 3, bottom right. In 2009, a few weeks before the foreseen start of the CNGS, a strong earthquake affected the area of Gran Sasso hitting severely the city and villages of L'Aquila. The LNGS experiments suffered only minor damages. The most important impact was on residents. Local activities, run preparation and processing of 2008 candidates, were stopped for more than a month. The CNGS run could nevertheless be started with only two weeks delay on June 1 st . Since then, the beam has been delivered with rather good efficiency, letting expect the order of 3.5 10 19 p.o.t. for the whole period. Processing of the 2009 sample has immediately started, in parallel with the end of the 2008 analysis.

Conclusions

After two short runs in 2006 and 2007, OPERA started significant data taking in 2008 when about 1700 neutrinos interacted in the target bricks. The Collaboration is finishing the extraction of data from the emulsions and their analysis, locating the final sample of vertices for   candidate search. Charm induced events study will be an important tool to improve control of efficiencies and background. A new physics run has started in June 2009, 3.5 10 19 protons on target could be delivered in about 160 days and ~3600 events collected in the OPERA bricks. About 2 's will then be expected in the total sample 2008-2009, opening the way to the direct observation of     oscillations. To reach quickly its physics goal, OPERA relies on the CERN support to have the CNGS running at nominal intensity in the next years.

Figure 1 .

 1 Figure 1. On the left are shown two pictures of OPERA target bricks, a complete brick (top) and an exploded view of a brick (bottom)showing its structure and the CS films packaging. On the right, a picture of the OPERA detector shows the two target sections (black covers) and their spectrometers. One of the brick manipulators is seen operating along the second target block.

Figure 2 .

 2 Figure 2. Statistics of the brick processing activities at the time of the EPS-HEP 2009 conference are shown for the 2008 sample. Fluxes at LNGS and CS scanning centers (left plot) and at brick scanning laboratories (right plot) can be seen.

Figure 3 .

 3 Figure 3. An example of charm decay candidate with a single prong kink (left). A neutral charm decay candidate (top right) found after recovery of tracks found in only one of the two emulsion layers of the film, using single micro-tracks. Bottom right plots show the improvement of the distribution of impact parameters after this method was applied.


Marie-Noëlle De Noirfontaine
email: marie-noelle.de-noirfontaine@polytechnique.edu

Sandrine Tusseau-Nenez

Marcel Signes-Frehel

Gilles Gasecki

Caroline Girod-Labianca

Effect of phosphorus impurity on tricalcium silicate T1: from synthesis to structural characterization

Alite is the major compound of anhydrous Portland cement: it is composed of tricalcium silicate Ca 3 SiO 5 (C 3 S) modified in composition and crystal structure by ionic substitutions. Alite is also the main hydraulic phase of cement and the most important for subsequent strength development. Using raw meals (rich in Ca 3 P 2 O 8 ) as alternative fuels in cement plants raises the question about the effect of phosphorus on C 3 S and its consequences on reactivity with water. This paper deals with a systematic study of C 3 S triclinic T 1 polymorph doped with P 2 O 5 in the range 0 to 0.9 wt. %. All the samples were characterized by X-ray powder diffraction (XRD), scanning electron microscopy (SEM) and electron-microprobe analysis (EMPA). The appearance of a phase rich in phosphorus is shown. It displays a structure derivative of the α' H -Ca 2 SiO 4 polymorph, noted α' H -C 2 S(P). As phosphorus content increases, C 3 S is more and more decomposed into free lime and α' H -C 2 S(P).

The α' H phase was detected from 0.1 wt. % P 2 O 5 and located at the interfaces of C 3 S grains. Two identification keys are proposed in order to highlight the α' H -C 2 S(P) phase: the XRD angular window at 2θ Cu = 32.8 -33.2° and a smooth aspect on SEM micrographs.

I. Introduction

Cement is one of the most ancient building materials. Today it remains the most commonly used, with an annual production of about 2 billions tons in the world. Surprisingly, cement still requires basic researches to develop accurate characterization methods in order to understand its chemical and physical properties. Anhydrous Portland cement is a mixture of clinker and gypsum, the latter being used to delay the setting. The clinker is a heterogeneous material, composed of at least four phases. The two major phases are calcium silicates: tricalcium silicate Ca 3 SiO 5 (referred to as C 3 S) and dicalcium silicate Ca 2 SiO 4 (referred to as C 2 S). The two other phases are calcium aluminates Ca 3 Al 2 O 6 (C 3 A) and Ca 4 Al 2 Fe 2 O 10 (C 4 AF) § . In fact, most of the calcium silicate phases are not pure: they are observed as solid solutions, called alite and belite for the C 3 S and C 2 S basedphases respectively. Both calcium silicates generate the hydrates responsible for the mechanical properties of the hydrated cement. C 3 S reacts faster than C 2 S with water, and then predominantly participates in the short term strength.

The polymorphs actually observed depend on the nature and the concentration of impurities (also called minors) in the solid solutions [START_REF] Taylor | Cement Chemistry[END_REF] . These impurities, added either deliberately or accidentally, are introduced either by the raw material or by the fuel used for calcination. Due to their effects on the calcium silicate polymorphs, one observes an alteration of both hydration reaction and the final hydrated cement properties in terms of setting and mechanical resistance. For all these reasons, it appears as important to correlate the minor elements found in clinker with the cement reactivity.

Ordinary Portland cement always contains phosphorus in the range 0.2 to 0.3 weight percent (wt. %) P 2 O 5 1,** . The effect of phosphorus was studied since 1950 until the 1980's in order to validate the use of phosphorus-rich limestone quarries, such as the phosphatic rocks of West Uganda [START_REF] Nurse | The effect of phosphate on the constitution and hardening of Portland cement[END_REF][START_REF] Salge | Effect of phosphorus pentoxide on the constitution of Portland cement clinker[END_REF][START_REF] Gutt | The phase composition of Portland cement clinker[END_REF][START_REF] Halicz | The influence of P 2 O 5 on clinker reactions[END_REF] . These authors investigated clinkers with phosphorus concentration above 1 wt. % P 2 O 5 .

The major effect of phosphorus addition is to decrease the alite/belite ratio, with a strong deterioration of the mechanical properties of the hydrated cement, since alite is the main hydraulic phase in clinker. For each additional of P 2 O 5 above 1 wt. %, the alite concentration decreases with § using the abbreviated oxide notation: C=CaO, S=SiO 2 , A=Al 2 O 3 , F=Fe 2 O 3 , H=H 2 O, P=P 2 O 5 ** Unlike the phosphatic cements, which exhibit high phosphorus content and distinct chemical species (as C 3 P), ordinary Portland cements contain only a low phosphorus concentration. 9.9 wt. % whereas the belite concentration increases with 10.9 wt. %. Above 2.25 wt. % P 2 O 5 , the clinker is no more acceptable for cement production [START_REF] Nurse | The effect of phosphate on the constitution and hardening of Portland cement[END_REF] .

Few studies are related to the effect of phosphorus below 1 wt. % P 2 O 5 [START_REF] Salge | Effect of phosphorus pentoxide on the constitution of Portland cement clinker[END_REF][START_REF] Gutt | The phase composition of Portland cement clinker[END_REF][START_REF] Halicz | The influence of P 2 O 5 on clinker reactions[END_REF] . Since 1998, raw meals are used as alternative fuels in cement plants. The ashes of raw meals (rich in Ca 3 P 2 O 8 , referred to as C 3 P) produced in the furnace during the clinker production are the origin of phosphorus incorporation into the phases of clinker. Therefore, the opened question of the effect of phosphorus in small quantities became subject for discussion. Above 0.5 wt. % P 2 O 5 , Kwon et al. [START_REF] Kwon | Effect of P 2 O 5 and chloride on clinkering reaction[END_REF] observe the decomposition of alite into belite and free lime. Phosphorus is located in the two calcium silicates, preferentially in belite [START_REF] Ghose | Distribution of minor elements in cement clinkers -macroscopic and microscopic variations[END_REF][START_REF] Kolovos | Study of clinker dopped with P and S compounds[END_REF] . However, some authors suggest a possible effect of very low contents of phosphorus on the tricalcium silicate reactivity [START_REF] Salge | Effect of phosphorus pentoxide on the constitution of Portland cement clinker[END_REF] .

Some studies on synthetic silicates samples are dedicated to the structural modifications induced by impurities ( Whatever the nature of the various impurities added, phosphorus induces a structural transition from the monoclinic β-C 2 S polymorph to the orthorhombic α' (α' H and α' L ) polymorphs, or to the hexagonal α polymorph in a minor way. Using X-ray diffraction on single crystal, Saalfeld and Klaska 9 investigated the structure of a C 2 S sample doped with phosphorus (6C 2 S.1C 3 P): they discovered a superstructure along b axis of the α' H basic structure previously determined [START_REF] Eysel | Polymorphism and Solid Solution of Ca 2 GeO 4 and Ca 2 SiO 4[END_REF][START_REF] Catti | Order disorder in the α'(Ca,Sr) 2 SiO 4 solid solution: a structural and statistical thermodynamic analysis[END_REF] . Using synchrotron X-ray powder diffraction, Mumme et al. [START_REF] Mumme | Rietveld crystal structure refinements, crystal chemistry and calculated powder diffraction data for the polymorphs of dicalcium silicate and related phases[END_REF] studied the stabilized structures of C 2 S doped with the only phosphorus impurity. They found two possible α' H structures depending on the amount of phosphorus: the basic structure for C 2 S + 5% mol C 3 P and the superstructure of Saalfeld † † for C 2 S + 10% mol C 3 P (6C 2 S.1C 3 P). Fukuda et al. [START_REF] Fukuda | Structure and Microstructure Changes in Phosphorous-Bearing Ca 2 SiO 4 Solid Solutions[END_REF] studied by TEM the αα' phase transitions in various belites as a function of P/Si ratio. Concerning C 3 S, the literature exhibits only one study of alites with low phosphorus concentration [START_REF] Diouri | Stable Ca 3 SiO 5 solid solution containing manganese and phosphorus[END_REF] Unfortunately, both the nature and the concentration of other impurities (such as Mn 2 O 3 , Fe 2 O 3 and Cr 2 O 3 ) vary between the various studies, and no overall conclusion can be drawn † † The superstructure of Saalfeld is referred to as "α-C 2 S" in the paper of Mumme.

concerning the solubility limit of phosphorus. To our knowledge, no systematic study is found in the literature devoted to the relation between the localization of phosphorus in T1 C 3 S polymorph and the properties of hydrated products for low phosphorus concentration. Therefore, in order to avoid possible crossed effect of impurities, and as a starting point for subsequent studies varying the impurities, we have chosen to investigate in this paper an alite with phosphorus as the only impurity.

This paper deals with a systematic structural study of tricalcium silicate T1 doped between 0 and 0.9 wt. % P 2 O 5 by X-ray diffraction analysis (XRD), together with scanning electron microscopy (SEM coupled with EDS analysis) and Castaing electron micro-probe analysis (EMPA).

II. Experimental procedure (1) Sample preparation

The tricalcium silicate samples were doped between 0 and 0.9 wt. % P 2 O 5 . The starting powders were tricalcium phosphate Ca 3 P 2 O 8 (VWR, VWR Prolabo reference 22420237, Fontenay sous Bois, France) and tricalcium silicate C 3 S (with a specific area of 370 m 2 .kg -1 , synthesized by G. Gasecki, CTG, Italcementi Group). Preliminary, Ca 3 P 2 O 8 powder was passed through a 80 µm sieve until refusal. For each doped sample, the experimental procedure was as follows. First, the dried powders were mixed together in stochiometric quantities. In a further step, the mixture was passed through a 250 µm sieve until refusal. This operation was repeated five times. Then, in order to get pellets, 10 grams of the resulting powders were uniaxially pressed during 25 seconds; the uniaxial pressure was 5 and 7 tons for 0 -0.5 and 0.7 -0.9 wt. % P 2 O 5 doped samples respectively.

The pellets were sintered in an electrical furnace with a heating rate of 30°C/min, held at 1450°C during 6.5h and then quenched in air, in order to avoid C 3 S retrogradation into C 2 S and free lime (referred to as f-CaO). The chemical homogenization of the mixtures was optimized by grinding the resulting pellets, pressed and sintered one time again.

In order to control the exact chemical composition and the free-lime content of the synthesized samples, the sintered pellets were ground with a mean particle size of 80 μm required for both the X-ray fluorescence and the ethylene glycol methods. The chemical composition (wt. %), given in Table II, was determined by X-ray fluorescence (XRF, Model PW2440, PANalytical, Almelo, the Netherlands). The unreacted lime (free lime, f-CaO) was determined according to the standard ethylene glycol extraction method [START_REF] Arjunan | Rapid techniques for determination of free lime and free magnesia in cement clinker and portlandite in hydrates[END_REF] . The results are summarized in Table III. A small decrease is observed in the range 0 -0.5 wt. % P 2 O 5 and a strong increase above 0.5 wt.

% P 2 O 5 . (

2) Structural analysis: X-ray powder diffraction data collection and Rietveld refinements

Sintered pellets were ground down to 40 μm mean particle size. X-ray powder diffraction was performed under the same conditions for all the samples. An X-ray powder diffractometer (Model X'Pert PRO MPD, PANalytical, Almelo, the Netherlands) in Bragg Brentano geometry (θ/θ) was used combined with a fast detector based on real time multiple strip (RTMS) technology (X'Celerator). For the purpose of an unambiguous phase identification, the powder pattern of the sample with the highest P 2 O 5 concentration (0.9 %) was also taken at higher resolution with a diffractometer (X'Pert PRO MPD, PANalytical), equipped with an incident beam monochromator and a fast detector (X'Celerator). Hereafter these two experimental setups -low and high resolutionare respectively referred to LR and HR. All the experimental settings and conditions are summarized in Table IV. (

3) Microstructural analysis: SEM observations coupled to EDS and Castaing microprobe

The microstructural and morphological features were observed on polished sections of the pellets, previously embedded in an epoxy resin by vacuum impregnation, and then coated with a layer of carbon to avoid charging under the electron beam.

In order to determine the distribution of phosphorus in the doped tricalcium silicate samples, a scanning electron microscope (SEM) equipped with a field emission gun (Model LEO 1530, Carl Zeiss SMT, Oberkochen, Germany), coupled to an energy dispersion X-ray analysis, EDS (Model Prism IMIX, Princeton Gamma-Tech Instruments, Princeton, USA), was used. To perform a local chemical analysis of each sample, more than 100 locations were analyzed using EDS at 15 kV accelerating voltage. The secondary electron images (predominant topographic contrast) were taken using 8 kV accelerating voltage.

To precise the localisation of phosphorus in samples, X-ray maps were accumulated with a Castaing microprobe (Model SX 100, CAMECA, Gennevilliers, France) equipped with WDS spectrometers. The WDS analyses were performed at 15 kV with a 40 nA beam current. The elements considered were calcium, silicon, oxygen and phosphorus.

III. Results

(1) X-ray diffraction analysis

(A) Phase identification: Pure C 3 S sample contains the expected T 1 triclinic polymorph (Fig. 1), with its two characteristic triplets (Fig. 2) in the two angular windows 2θ Cu =31 -33.5° and 2θ Cu = 51 -52.3° respectively referred to as W3 and W5 in the study of Courtial et al. [START_REF] Courtial | Polymorphism of Tricalcium Silicate in Portland Cement: a fast visual identification of structure and superstructure[END_REF] . The positions of the C 3 S Bragg lines are well reproduced using the C 3 S triclinic unit cell parameters of the powder diffraction study of Regourd et al. [START_REF] Regourd | Détermination des réseaux de cristaux microscopiques. Application aux différentes formes du silicate tricalcique[END_REF]23 . The C 3 S Bragg lines are indexed on the basis of the structural model determined by Golovastikov et al. [START_REF] Golovastikov | Crystal Structure of the Tricalcium Silicate 3CaO.SiO 2 =C 3 S[END_REF]25 . The indexation of the lines of the two triplets of the W3 and W5 windows is given by Fig. The evolution of the XRD patterns with increasing P 2 O 5 content is given in Fig. 3a.

Whatever the P 2 O 5 content, the same triclinic T 1 type of polymorph is always observed. Below 0.5 wt. % P 2 O 5, the whole pattern is explained using the same phases as in the pure sample. From 0.5 wt. % P 2 O 5 upwards, rather intense and broad peaks are observed, the two more intense of them being located respectively between 2θ Cu = 30.9 -31.3° and 2θ Cu = 32.9 -33.1° (inside the W3 angular window) as shown by arrows in Fig. 3(a, b-c). The Bragg line (001) of portlandite 27 Ca(OH) 2 is also identified at 2θ Cu = 17.98°, with an increasing intensity along with P 2 O 5 content (Fig. 3d) ‡ ‡ . Therefore, in our samples (detailed in § III. The next point is now the origin of the broadening of the two peaks 1 and 2 of Fig. 3, not observed in the pure sample, and therefore referred to as the "new peaks" in the following. An additional XRD experiment was performed using higher resolution conditions (cf. Table IV, HR experimental setup) on the sample with the highest impurity content (0.9 wt. % P 2 O 5 ). Figure 4 superimposes the data in the W3 window for the LR and HR experimental setups. In order to perform the comparison, the K α2 contribution of the LR pattern was previously subtracted by a numerical treatment using EVA software. Two distinct peaks in the 2θ Cu = 32.9 -33.1° range are ‡ ‡ The Bragg line (-211) of C 3 S (intensity = 0.2%) can be neglected compared to the Ca(OH) 2 one (intensity = 72%).

actually clearly observed in the HR experiment. The line width of these peaks is still higher than that of the C 3 S lines of the same pattern. Such a peak broadening may be due either to a size-effect, and/or to a distribution of various chemical composition and/or internal strain. (B) Rietveld quantification: For the series of doped samples, the set of XRD data collected with the LR experimental setup was systematically analyzed quantitatively using the Rietveld methodology [START_REF] Rietveld | A Profile Refinement Method for Nuclear and Magnetic Structures[END_REF][START_REF]The Rietveld Method[END_REF] . The refined parameters were scale factors, sample displacement, background as Chebychev polynomial of the fifth order, crystallite size and unit cell parameters of all the phases.

The atomic positions and temperature factors were kept constant in all the crystal structures.

The Saalfeld structure of the α' H -C 2 S phase [START_REF] Saalfeld | The crystal structure of 6 Ca 2 SiO 4 .1 Ca 3 (PO 4 ) 2[END_REF] , determined by the authors using single crystal studies, introduces a unit cell with so-called TO 4 tetrahedra instead of SiO 4 tetrahedra § § . Powder diffraction is much less sensitive than single crystal diffraction to such details. Therefore, we use here a simplified model: all these tetrahedra are taken only as SiO 4 tetrahedra. The four following structural models are used:

-C 3 S: model of Golovastikov et al. [START_REF] Golovastikov | Crystal Structure of the Tricalcium Silicate 3CaO.SiO 2 =C 3 S[END_REF] ,

-CaO lime: model of Wyckoff [START_REF] Wyckoff | Crystal Structures[END_REF] (NaCl structural type),

-portlandite: model of Petch [START_REF] Petch | The hydrogen positions in portlandite, Ca(OH) 2 , as indicated by the electron distribution[END_REF] , -α' H -C 2 S: the Saalfeld and Klaska 9 simplified model as mentioned above.

The α' H -C 2 S phase is taken into account only from 0.3 wt. % P 2 O 5 upwards.

The good agreement of the refinements validates the presence of these four phases. Figure 5 reproduces the refinement for the most doped sample and shows the good treatment of the experimental doublet of Bragg lines at 2θ Cu = 33° (W3 window).

As the P 2 O 5 content increases from 0.3 wt. % P 2 O 5 upwards, the quantitative phase analysis (Fig. 5 and Table V) shows a diminution of the amount of C 3 S phase correlated with an increase of the α' H -C 2 S, f-CaO and portlandite phases. It suggests a decomposition of C 3 S into α' H -C 2 S and f-CaO.

No significant effect on the evolution of the unit cell parameters of C 3 S is detected. Due to the unfiltered K α1,α2 radiation and to the very low concentration of the α' H -C 2 S phase, the resolution is not sufficient to discuss a meaningful evolution of the unit cell parameters of the α' H -C 2 S phase (Table VI). However, from 0.5 wt. % P 2 O 5 upwards, the unit cell parameters are close to those of Saalfeld and Klaska [START_REF] Saalfeld | The crystal structure of 6 Ca 2 SiO 4 .1 Ca 3 (PO 4 ) 2[END_REF] .

In conclusion, as already shown by previous studies (cf. Table I), phosphorus stabilises the α' H -C 2 S phase, hereafter referred to as the α' H -C 2 S(P) phase. § § These TO 4 tetrahedra have to be understood as a weighted average between the SiO 4 and PO 4 tetrahedra. The problem with such an average is the electric balance due to the replacement of Si 4+ ions by P 5+ ions. In order to keep the electric neutrality Ca 2+ vacancies are introduced using a population x Ca <1 for some calcium ions. (

2) Microstructural and chemical analysis (SEM/EDS and EMPA)

Figure 6 shows secondary electron images and microanalyses of pure C 3 S (Fig. 6a) and C 3 S doped with 0.1 and 0.3 wt. % P 2 O 5 (Figs. 6b-c).

(A) Pure sample: Figure 6a shows (in grey) the grain clusters of the sample. EDS analyses made in several parts of the sample (points 1 and 2 in Fig. 6a) show calcium, silicon, oxygen and carbon (coating) only. Additional EMPA X-ray maps (Fig. 7a) attest the chemical homogeneity of the sample. Thus, according to XRD analysis, the sample contains only the expected pure C 3 S phase. (

2) α' H -C 2 S(P) phase:

The phase is identified for different P 2 O 5 contents according to the three experiments:

-XRD: 0.5 wt. % (Fig. 3)

-EMPA: 0.3 wt. % (Fig. 7)

-SEM: 0.1 wt. % (Fig. 6b) This is due to the different detection thresholds of the three techniques. We show that α' H -C 2 S(P) would appear for an addition of only 0.1 wt. % P 2 O 5 . Diouri et al. [START_REF] Diouri | Stable Ca 3 SiO 5 solid solution containing manganese and phosphorus[END_REF] observe the retrogradation of C 3 S into C 2 S and CaO above 1.5 wt. % of P 2 O 5 when P and Mn impurities are present (Table. I).

These authors showed that the coupled impurities (P, Mn) stabilize the M3 large superstructure instead of the T1 C 3 S polymorph. Indeed, Mn impurity promotes the formation of the monoclinic modification [START_REF] Puertas | Influence of the kiln atmosphere on manganese solid solution in Ca 3 SiO 5 and Ca 2 SiO 4[END_REF] . Our paper shows a lower solubility limit in T1 polymorph (ten times smaller), when P is the only impurity.

The topographic contrast is optimized for a voltage of 8 kV. As lower acceleration voltage excites electrons only from the surface, this means that the α' H -C 2 S(P) phase is located at the surface of the C 3 S grains.

The detection threshold of the EDS analyses is estimated about 1 wt. % of an element.

Adding only 0.1 wt. % P 2 O 5 , phosphorus is detected in α' H -C 2 S(P) phase, suggesting that this phase is enriched in phosphorus from the beginning. The α' H -C 2 S(P) proportion increases and the phase covers more and more C 3 S grains as the P 2 O 5 content increases. At this stage of the study, it is not possible to precise whether α' H -C 2 S(P) is a stoechiometric compound or a solid solution with an increasing substitution of Si 4+ by P 5+ ions. However, these results are consistent with our hydration experiments -to be published elsewhere -which clearly show an increasing of the setting time along with the phosphorus content.

One may wonder why the α' H -C 2 S(P) layer appears smooth. Several hypotheses can be suggested. A first hypothesis is that the layer crystallized after being melted during the synthesis of the sample (1450°C). In this case, this is consistent with the broad XRD peaks observed for this phase. Another hypothesis is a possible effect of different hardness of C 3 S and C 2 S phases. In this case, the topological effect may be a result of the polishing of the sample for the SEM experiment, with a similar effect during the grinding process for the sample for X-ray diffraction experiments.

The hardness (H) of C 3 S and C 2 S phases are in the same range (H ~ 8 -9 GPa) [START_REF] Velez | Determination by nanoindentation of elastic modulus and hardness of pure constituents of Portland cement clinker[END_REF] , which reinforces our first hypothesis. Imaging the so-called smooth phase may be a handy tool for the α' H -C 2 S(P) identification.

(3) Lime and portlandite:

X-ray diffraction shows that lime is found either as free lime f-CaO and as portlandite Ca(OH) 2 , i.e. partially hydrated. However the free lime test usually performed on cement compounds is only able to give the overall composition without being able to distinguish between hydrated and anhydrous lime (Table III).

V. Conclusions

A systematic study of the effect of phosphorus addition to pure C 3 S in the range 0.1 to 0.9 wt. % P 2 O 5 was performed. Our results show that adding phosphorus (alone) from 0.1 wt. % P 2 O 5 causes a partial decomposition of C 3 S into α' H -C 2 S and CaO phases. This indicates (i) a low solubility limit of phosphorus in T1 C 3 S (≤ 0.1 wt. % P 2 O 5 ) and (ii) supports the idea that phosphorus impurity stabilizes α' H -C 2 S polymorph. The content of phosphorus in the α' H -C 2 S(P) phase is more than 1 wt. % P 2 O 5 . As P 2 O 5 content increases, the α' H -C 2 S(P) phase appears as layer covering more and more C 3 S grains. Further quantitative microprobe analyses may be relevant in order to precise the chemical composition of α' H -C 2 S(P).

We propose two identification keys in order to highlight the α' H -C 2 S(P) phase:

-by XRD: the angular window 2θ Cu = 32.8 -33.2° exhibits three characteristic Bragg lines that can be measured using a high resolution setup.

-by SEM: the smooth aspect of the α' H -C 2 S(P) superficial layer, which can be observed in topological contrast conditions at low electron energy (8 keV).

Further experiments (at the nanometric scale) such as TEM or NMR would be necessary (i)

to precise the solid limit of solubility of phosphorus in C 3 S with samples doped between 0 and 0.1% This study is the first step towards a better characterisation of Portland cement doped with phosphorus and a better understanding of its effect on hydration kinetics and mechanical properties.

2 .

 2 Fig.1.

Fig. 1 .Fig. 2 .

 12 Fig. 1. X-ray diffraction pattern of the pure C 3 S sample (T 1 triclinic polymorph) with the LR experimental setup. The arrow shows the characteristic line (200) of free lime (f-CaO) at 2θ Cu = 37.36°.

Fig. 3 .

 3 Fig. 3. (a) XRD patterns of the samples doped with various P 2 O 5 contents (0 -0.9 wt. % P 2 O 5 ): LR experimental setup. The arrows (1 and 2) show the more intense new peaks, which appear above 0.3 wt. % P 2 O 5 . (b) 2θ Cu = 30.7 -31.5°; (c) 2θ Cu = 32.7 -33.5°; (d) Bragg line (001) of portlandite about 2θ Cu = 17.98°.

Fig. 4 .

 4 Fig. 4. W3 window: XRD patterns of the sample doped with 0.9 wt. % P 2 O 5 : LR and HR experimental setups. In the LR case, a data treatment was performed in order to subtract the K α2 contribution. The vertical arrows and points show the indexation of the more intense Bragg lines of pure C 3 S and α' H -C 2 S polymorphs respectively.The presence of this experimental doublet about 2θ Cu = 33° makes easier the phase identification of the additional phase. A systematic phase research leads to the identification of the structure proposed by Saalfeld and Klaska 9,28 : a compound 6C 2 S.1C 3 P (i.e. about 10.6 wt. % C 3 P), displaying a superstructure of the α' H -C 2 S polymorph. The doublet is indexed with the Bragg lines doublet (080 and 340 at d = 0.27136 nm) and the 171 Bragg line (d = 0.270452 nm) of the structural model. The other intense lines (142, 202, 321) of α' H -C 2 S are mixed with strong C 3 S lines (Fig.4).The visual identification described here is based on the detection of two or three Bragg lines: the only lines clearly separated from the others. However, in the next paragraph (III.1.B), this result will be validated on the whole pattern using Rietveld analysis. To conclude, the doublet about 2θ Cu = 33° containing the intense Bragg lines of the Saalfeld structure, and none of the intense C 3 S lines, is a useful key for a visual identification of the α' H -C 2 S phase.

Fig. 5 .

 5 Fig. 5. Rietveld refinement of XRD data of the sample doped with 0.9 wt. % P 2 O 5 (LR experimental setup), with the model of Golovastikov for C 3 S and the model of Saalfeld simplified here for α' H -C 2 S. The arrows mark the characteristic peaks of α' H -C 2 S (cf. figure 3a). From top to bottom are represented: the observed (black curve) and calculated (grey) XRD patterns, the calculated contribution of α' H -C 2 S (red line), the difference plot between observed and calculated data, the Bragg reflection markers. From top to bottom, these markers correspond to C 3 S, lime, portlandite and α' H -C 2 S.

(

  B) Doped samples: From 0.1 wt. % P 2 O 5 upwards, secondary electron images show several levels of grey. Up to 0.9 wt. % P 2 O 5, a phase with a very smooth appearance (no porosity, no polishing lines and no cracking) covers more and more the C 3 S grain clusters. It appears in clearer grey than that of C 3 S phase (see Fig.6b-c, labels 4, 5 and 7). The contrast between the two phases is optimized when decreasing the voltage (from 15 to 8 kV), which suggests the presence of a thin layer covering C 3 S grain clusters. EDS analyses in several regions of this smooth phase, as illustrated in Fig.6b-cwith the spectra numbered 4, 5 and 7, show the presence of Ca, Si, O and P in this layer. No phosphorus is detected in C 3 S darker grain clusters (see Fig 6b-c, labels 3 and 6).Above 0.5 wt. % P 2 O 5 , free lime clusters dispersed in the whole sample are also observed in dark grey (their characteristic cubic morphology can be observed in Fig.6c, label 8). Additional X-ray maps with Castaing microprobe were performed in order to precise the localization of phosphorus.

Figure

  Figure7bshows the case of the C 3 S sample doped with 0.3 wt. % P 2 O 5 : phosphorus clearly accumulates in grain boundaries of C 3 S grains. As the amount of phosphorus increases, a thin layer rich in phosphorus progressively covers the C 3 S grain clusters, as was seen in SEM observations. This new layer is attributed to the phase observed in our XRD study (III.1.B), that we attribute to the retrogradation of the C 3 S into α' H -C 2 S(P) and free lime.

Fig. 6 .Fig. 7 .

 67 Fig. 6. Scanning electron micrographs (secondary electron images): (a) pure C 3 S (b) C 3 S doped with 0.1 wt. % P 2 O 5 and (c) 0.9 wt. % P 2 O 5 . The regions of the EDS analyses are labelled from 1 to 8 in the SEM micrographs.

  and (ii) to validate the substitution of Si 4+ ions by P 5+ ions in α' H -C 2 S, as suggested by Saalfeld and Klaska: 2SiO 4 → 2PO 4 + Va Ca ( Va = vacancy).

  Table I). Most of the studies deal with synthetic C 2 S doped samples, with possible crossed effects of the various impurities added (P 2 O 5 , coupled with Fe 2 O 3 or Cr 2 O 3 ).

  . Once again, P 2 O 5 impurity is coupled with another impurity: Mn 2 O 3 . The authors observed M3 polymorph for alite. Above 1.56 wt. % P 2 O 5 , alite is decomposed into C 2 S and lime. When P 2 O 5 content increases, the β-C 2 S polymorph is converted into the α' polymorph, as previously shown.

Table I . Phosphorus effects on the structure of alite (impure C 3 S) and belite (impure C 2 S): stabilized polymorphs versus chemical composition of the samples. Mumme et al. only reported the expected P 2 O 5 content (no chemical analysis after synthesis is mentioned). The type of α' polymorph is specified when sufficient crystallographic data is given by the authors

 I means that β is major than γ polymorph. β = α' means that β and γ polymorphs are in equal quantities. Four single crystals investigated by EMPA, lower and upper contents are mentioned here.

	Sample			Chemical composition (wt. %)				Stabilized polymorph §	References
		CaO	SiO 2	P 2 O 5 Mn 2 O 3 Fe 2 O 3 Cr 2 O 3 Al 2 O 3 K 2 O	C 2 S	C 3 S
	C 2 S	65.12	34.88	0	0	0	0	0	0	β > γ		Benarchid et al. 15
	C 2 S Belite Belite Belite Belite	65.12 64.56 62.88 62.25 62.32	34.88 34.58 33.68 33.34 33.38	0 0.41 1.66 2.07 2.08	0 0 0 0 0	0 0 0 2.33 0	0 0.44 1.77 0 2.22	0 0 0 0 0	0 0 0 0 0	γ > β β > γ β β β = α'		Qotaibi et al. 16 Qotaibi et al. 16 Qotaibi et al. 16 Benarchid et al. 15 Qotaibi et al. 16
	Belite Belite Belite Belite Belite Belite Belite Belite Belite	63.27 59.48 59.34 63.44 62.14 61.81 53.42 61.9-	32.19 31.86 31.79 31.08 29.71 28.64 28.62 26.3-	3.54 4.18 4.17 4.90 ∼ 5 6.47 8.30 8.45 7.1-	0 0 0 0 0 0 0 0	0.68 0 4.69 0.67 0.63 0.69 9.50 0	0 4.48 0 0 0 0 0 0	0.11 0 0 0.12 0.13 0.17 0 0	0.12 0 0 0.12 0.25 0.20 0 0	α' L α' > β α' α' L α' H α' L α' L α > α' α' H		Fukuda et al. 13 Qotaibi et al. 16 Benarchid et al. 15 Fukuda et al. 13 Mumme et al. 12 Fukuda et al. 13 Fukuda et al. 13 Benarchid et al. 15 Saalfeld et al. 9
		63.0	28.5	11.8
	Belite Belite	60.04	21.94	∼ 10 17.15	0	0.61	0	0.18	0.41	α' H α		Mumme et al. 12 Fukuda et al. 13
	Alite	73.26	26.08	0.31	0.35	0	0	0	0	-	M3	Diouri et al. 14
	Alite	72.84	25.84	0.62	0.69	0	0	0	0	-	M3	Diouri et al. 14
	Alite	71.57	25.12	1.56	1.73	0	0	0	0	β	M3	Diouri et al. 14
	Alite Alite	69.45 67.30	23.92 22.70	3.14 4.73	3.48 5.26	0 0	0 0	0 0	0 0	β β = α'	--	Diouri et al. 14 Diouri et al. 14
	§ β > γ

Table II . Chemical analysis (XRF) for the C 3 S samples doped with varying P 2 O 5 contents. In the following of the text, the P 2 O 5 contents of the samples are referred to as 0.1 until 0.9 wt. % (7 th column)

 II

	CaO	SiO 2	Al 2 O 3	Fe 2 O 3	P 2 O 5	Loss on ignition	P 2 O 5 range
	(wt. %)	(wt. %)	(wt. %)	(wt. %)	(wt. %)	(wt. %)	(wt. %)
	73.44	25.98	0.09	0.02	0.00	0.47	0.0
	73.36	25.88	0.11	0.02	0.09	0.54	0.1
	73.25	25.75	0.09	0.01	0.31	0.59	0.3
	73.17	25.65	0.10	0.00	0.50	0.58	0.5
	73.18	25.53	0.10	0.00	0.71	0.47	0.7
	73.14	25.39	0.09	0.01	0.92	0.45	0.9

Table III . Free lime contents (f-CaO) in the C 3 S samples doped with varying P 2 O 5 contents. The experimental uncertainty was established at 16% in a range of observed values

 III

	P 2 O 5 (wt. %)	0.0	0.1	0.3	0.5	0.7	0.9
	f-CaO (wt. %) 0.8 ± 0.1	0.6 ± 0.1	0.4 ± 0.1	0.8 ± 0.1	1.5 ± 0.2	2.2 ± 0.4

Table IV . Experimental settings for XRD analysis for all the samples (LR) and for the 0.9 wt. % P 2 O 5 doped C 3 S sample (HR)

 IV

	Experimental setup	LR	HR
	Tube	Cu	Cu
	Generator settings (kV, mA)	45, 40	45, 40
	Incident filter	Ni	None
	Incident monochromator	none	curved Ge (111)
	Incident radiation	Cu K α1, α2	Cu K α1
	Incident Soller slits (rad)	0.04	0.02
	Incident divergence slit (°)	0.25	0.5
	Mask (mm)	10	10
	Incident anti-scattering slit (°)	0.5	1
	Sample holder	spinning	spinning
	Anti-scattering slit (mm)	5	5
	Soller slits (rad)	0.04	0.02
	X'Celerator detector aperture (°2θ)	2.122	2.022
	Scan type	continuous	continuous
	Range (°2θ)	10 -70	10 -70
	Step size (°2θ)	0.0167	0.0084
	Scan step time (hour)	0.5	13
	Phase identifications were performed using EVA software (version 13, Bruker-AXS,

Karlsruhe, Germany, 1996-2007)

and JCPDS -International Centre for Diffraction Data® Powder Diffraction File (PDF-2, JCPDS-ICDD, Newtown Square, PA). Rietveld refinements were performed using TOPAS 3 software (TOPAS, version 3, Bruker-AXS, Karlsruhe, Germany, 1996-2007) based on the fundamental parameters approach

[START_REF] Cheary | A fundamental parameters approach to X-ray Line-Profile Fitting[END_REF]

.

  1.C), f-CaO is in fact hydrated into portlandite. The broadening of the portlandite lines is related to a nanometric grain size.

		7000	C 3 S														600
		6000	C 3 S + 0.1% P 2 O 5 C 3 S + 0.3% P 2 O 5													0% 0.1%
	Counts	3000 4000 5000	C 3 S + 0.5% P 2 O 5 C 3 S + 0.7% P 2 O 5 C 3 S + 0.9% P 2 O 5											Counts	500 400	0.3% 0.5% 0.7% 0.9%	1
																		300
		2000						2
						1
		1000																200
		0																30,7	30,8	30,9	31,0	31,1	31,2	31,3	31,4	31,5
		27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42		2 theta-Cu (deg.)
								2 theta-Cu (deg.)
									(a)										(b)
																		700
				2800
				2400														600
				2000														500
			Counts	1600				2									Counts	400
				1200
																		300
				800
				400														200
				32,7	32,8	32,9	33,0	33,1	33,2		33,3	33,4	33,5				17,6	17,7	17,8	17,9	18,0	18,1	18,2	18,3	18,4
								2 theta-Cu (deg.)									2 theta-Cu (deg.)
									(c)										(d)

Table V . Rietveld analyses of the XRD data (LR experimental setup) of the C 3 S doped samples: quantitative phase analyses and resulting criteria of fits (goodness of fit -GOF -and R Bragg )

 V

	P 2 O 5 (wt. %)	0.0	0.1	0.3	0.5	0.7	0.9
	C 3 S (wt. %) α' H -C 2 S (wt. %)	99.3(12) 98.65(20) 96.23(39) 93.07(38) 89.72(34) 85.30(31) --2.75(35) 5.50(34) 7.92(30) 11.35(27)
	CaO (wt. %)	0.44(11)	0.36(11)	0.36(10) 0.310(98) 0.316(99) 0.232(81)
	Portlandite (wt. %) 0.266(59) 0.99(17)	0.66(17)	1.11(16)	2.05(16)	3.11(10)
	GOF	2.06	2.12	1.95	1.96	2.01	1.92
	R Bragg (C 3 S)	4.79	4.88	4.06	4.12	4.76	4.26
	R Bragg (α' H -C 2 S)	-	-	2.67	3.11	3.83	3.81
	R Bragg (CaO)	3.29	3.11	2.50	2.51	2.49	1.78
	R Bragg (Portlandite)	3.23	3.19	2.67	2.55	2.38	2.66

Table VI . Rietveld analyses of the XRD data (LR experimental setup) of the C 3 S doped samples: evolution of the unit cell parameters of doped α' H -C 2 S phase. Comparison with the single crystal study of Saalfeld

 VI

	Doped α' H -C 2 S phase	P 2 O 5 (wt. %)	a (nm)	b (nm)	c (nm)	α = β = γ (deg.)	V (nm 3 )
	This study	0.3	0.9385(18)	2.1488(38)	0.6815(13)	90	1.3744(44)
	This study	0.5	0.939(15)	2.1714(29)	0.68143(66)	90	1.3893(32)
	This study	0.7	0.93918(61)	2.1740(12)	0.68144(30)	90	1.3913(14)
	This study	0.9	0.93930(36)	2.17356(72) 0.68123(18)	90	1.39081(79)
	Saalfeld and Klaska 9	∼ 7-12	0.940(8)	2.171(2)	0.683(3)	90	1.39382(5)

Acknowledgments

The authors are grateful to Dr. V. Pontikis (CEA Saclay, France) for his fruitful discussions and advice during this work and to M. B. Bollotte (Italcementi Group) for his cooperation and financial support. The authors also warmly thank Dr. F. Dunstetter (CEA Saclay, France) for his constructive remarks and his critical reading of the manuscript. Dr L. Pinsard-Gaudard (ICMMO, University of Paris XI) performed the acquisition of the high resolution XRD pattern. A. Allavena-Valette (CECM, CNRS) and E. Leroy (LCMTR, CNRS) did their best to obtain the SEM and EMPA images. Many thanks to all of them.

This work was financially supported by CTG-Italcementi Group.


Andrés Véjar
email: andres.vejar@cran.uhp-nancy.fr

Iván Gómez-Casta

I Gómez-Castaño

Reparation as an emergent process in metabolic networks

Keywords: self-repair, catalysis, self-organization, (M, R)-systems

In biology, one of the most challenging problems is how the emergence of self-organization and operational closure are maintained through time. In this topic, phenomena like regulation, replication and reparation have to be defined in order to get a concept of self-organization. Up to now, reparation in metabolic networks has a non trivial description and many efforts have been made to investigate related concepts as closure existence or system dynamics. We propose a model where the coexistence of intermittent coupled dynamical systems allows the emergence of global reparation as a property of the whole network and, also, it is needed to maintain the normal function of the individuality in time.

Introduction

Different proposals in self-organization have as central idea the operation of a catalytic closure to start the process of differentiation from the environment [START_REF] Maturana | The tree of knowledge: The biological roots of human understanding[END_REF][START_REF] Maturana | De máquinas y seres vivos: Una teoría sobre la organización biológica[END_REF][START_REF] Kauffman | The Origins of Order: Self-organization and Selection in Evolution[END_REF][START_REF] Rosen | Life itself: a comprehensive inquiry into the nature, origin, and fabrication of life[END_REF]. For this, the basic concept of two basic molecules, one catalyzing the other to produce a new one, is one of the basic requirements to start an operational closure. All these types of models try to solve the problem of how catalytic closures are able to maintain it in time with an adequate quantity of catalyst molecules. Nonetheless, self-repairing of catalytic molecules in a chain of reactions remains an unsolved issue in theoretical biology.

A very precise molecular description of the pathways involved in self-repair at biological sciences is deeply described. Nonetheless, such types of specialized mechanism belong to a more complicated infrastructure that, at the beginning of life, with a limited number of species and functions, could be not possible to obtain [START_REF] Kauffman | Question 1: Origin of life and the living state. Origins of Life and Evolution of Biospheres[END_REF]. For this reason, simpler and more efficient mechanisms of self-repair had to emerge in the mutual interaction of simple catalytic species [START_REF] Smith | Universality in intermediary metabolism[END_REF]. A classical example of catalysis in biological systems are the enzymes, molecules encoded in highly conserved DNA or RNA templates that have a great importance for the maintenance of catalytic closures at the beginning of life, as well as in present times [START_REF] Ringe | How enzymes work[END_REF]. In this communication, we propose a model where the self-reparing catalytic properties in a cell can emerge as the result of interactions in the network. Even that enzymes production based on the transcription of DNA templates is very efficient, it seems that complicated multi-steps processes at the beginning of life are more difficult to obtain . By this phenomena, maybe the emergence of the first mechanisms of reparation (independent from DNA) can be due to this emergent process, a more simple and dynamic one.

Metabolic Repair

In Rosen's (M, R)-systems researches [START_REF] Louie | Kercel: Topology and Life Redux: Robert Rosen's Relational Diagrams of Living Systems[END_REF][START_REF] Baianu | Robert Rosen's Work and Complex Systems Biology[END_REF][START_REF] Letelier | Organizational invariance and metabolic closure: Analysis in terms of (M,R) systems[END_REF][START_REF] Carlos Letelier | Jorge Mpodozis: Autopoietic and (M,R) systems[END_REF][START_REF] Cornish-Bowden | Self-organization at the origin of life[END_REF], they generally try to solve the closure of an autonomous system by means of a switching route between mapping of mappings, but no time scales are considered. Some class of instantaneous reparation is needed by this type of modeling, and no satisfactory solutions can be given, because only the exis-tence of global mappings switching functions and inverses are a difficult mathematical problem [START_REF] Letelier | Organizational invariance and metabolic closure: Analysis in terms of (M,R) systems[END_REF]. The complexity of the (M, R)-systems can be analyzed with hyperset theory [START_REF] Chemero | Autonomy and hypersets[END_REF], to avoid the computational modeling of the autonomy in life systems.

Modeling

Be the process a f -→ b, where f is the catalizer of this reaction. If f has a lifespan, it is conditionated by its own degradation through time. When f is degradating, the output b is also gradually corrupted. If in an instant t the elements of a system are a and f , this state is expressed by {a, f } t . If the reaction time is p, a is joined with f t in an instant t to generate b f t , then the history of the system is {a,

f t } t , { f t+p , b f t } t+p .
If f t , n < t < m, is in a normal production state (not completly degradated), with n the starting production time, and m the complete degradation time, then the process can be described for the diagram:

↓ a ↑ b f t f n . . . f t f t+p . . . f m
For simplicity, if f has only two states N (normal) and D (degradated), the process has the followed transitions:

normal : {a, f N } t -→ { f D , b} t+p degradated : {a, f D } t -→ {a, f D } T >t
In order to maintain the process a f -→ b, for long time, another intermitent transition to repair f is needed, { f D , b} t → {b, f N } t+r , with process time r, then a part in the history of the process could be:

{a, f N } t , { f D , b} t+p , {b, f N } t+p+r
The intermitent process is showed in Fig. 1, and also in a state diagram in Fig. 2.

More precisely, in the modeling, the self-repair system is an intermitent coupled dynamical system that evolves at different time-scales, specially the production time-scale, the repair time-scale, and the parameter evolution time-scale.

Conclusions

In this work we discuss the concept of self-reparation in living systems, modeling the production and reparation of different coupled processes that coexist in different timescales. The feedback between systems in the network is maintained in intermitent oscillations. The study of long-term dynamics, is essential to show the self-reparation as an emergent behavior, and in our model, the self-reparation is vanished if we analyze only the short-term behavior.

input output ↓ ↑ ↓ ↑ limits • • • -• --• --• --• --• --• --• -• • • a b b a b b f N f D f N f D f N f D f N a b b a limits • • • -• --• --• --• --• --• --• -• • • ↑ ↓ ↑ time • • • t t

Fig. 1 Fig. 2

 12 Fig. 1 Diagram of evolution for the intermitent oscillatory processes of tranformation and reparation