Pedro Chahuara
email: pedro.chahuara@imag.fr

Anthony Fleury
email: anthony.fleury@mines-douai.fr

François Portet
email: francois.portet@imag.fr

Michel Vacher
email: michel.vacher@imag.fr

Using Markov Logic Network for On-line Activity Recognition from Non-Visual Home Automation Sensors

Keywords: Activity Recognition, Markov Logic Network, Support Vector Machine, Smart Home, Ambient Assisted Living

This paper presents the application of Markov Logic Networks(MLN) for the the recognition of Activities of Daily Living (ADL) in a smart home. We describe a procedure that uses raw data from non visual and non wearable sensors in order to create a classification model leveraging logic formal representation and probabilistic inference. SVM and Naive Bayes methods were used as baselines to compare the performance of our implementation, as they have proved to be highly efficient in classification tasks. The evaluation was carried out on a real smart home where 21 participants performed ADLs. Results show not only the appreciable capacities of MLN as a classifier, but also its potential to be easily integrable into a formal knowledge representation framework.

Introduction

In the Ambient Assisted Living domain there is a increased interest in automatic human activity recognition from sensors [START_REF] Tapia | Activity recognition in the home using simple and ubiquitous sensors[END_REF][START_REF] Storf | Rule-based activity recognition framework : Challenges, technique and learning[END_REF][START_REF] Van Kasteren | Bayesian activity recognition in residence for elders[END_REF]. Recognition of human activity is recognised as one important variable for human behaviour monitoring but it is also extensively studied for the provision of context-aware services in smart-phones and other smart objects [START_REF] Coutaz | Context is key[END_REF].

In this paper, we focus on the recognition of activity within the home which is a private space in which multiple sensors, actuators and home automation equipments coexist. This research is linked to the Sweet-Home project which aims at developing a complete framework to enable voice command in smart homes. In this framework, the interpretation of the orders and the decisions to be made depend on the context in which the user is. This context is composed, among other information, of the user's current activity which is essential for decision making. For instance, if the user utters "turn on the light", the action will be different if she is awaking in the middle of the night (in that case, the best action could be to provide low intensity light using the bedside lamp) or if she is dressing up in the morning (in that case, the best action could be to provide high intensity light using the ceiling lamp). Knowing whether the user is sleeping or dressing permits fine grain decision making and facilitate disambiguation of situations interpretation.

Most of the progresses made in the field of activity recognition come from the computer vision domain [START_REF] Aggarwal | Human activity analysis : A review[END_REF]. However, the installation of video cameras in the user's home is not only raising ethical questions [START_REF] Tapia | Activity recognition in the home using simple and ubiquitous sensors[END_REF], but is also rejected by some users [START_REF] Portet | Design and evaluation of a smart home voice interface for the elderly -acceptability and objection aspects[END_REF]. Other approaches rely on information from RFID tags [START_REF] Helaoui | A statistical-relational activity recognition framework for ambient assisted living systems[END_REF] and wearable devices [START_REF] Zappi | Activity recognition from on-body sensors : Accuracy-power trade-off by dynamic sensor selection[END_REF]. In the first case, putting RFID tags on objects makes fastidious the maintenance of the smart home since any new object implies technical manipulation to attach the corresponding sensor. The case of wearable sensors is sometimes not applicable when inhabitants do not want (or forget) to wear sensors all the time. Moreover, cost and dissemination of assistive technology would be more efficient if it is built on standard home automation technology with minimal technical addition. This is why, the solution developed in the Sweet-Home project is to complete conventional sensors for home automation (infrared presence detectors, switches, etc.) by microphones to allow the user to control her environment through voice recognition.

This type of environment imposes constraints on the sensors and the technology used for recognition. Indeed, information provided by the sensor for activity recognition is indirect (no worn sensors for localisation), heterogeneous (from numerical to categorical), transient (no continuous recording), noisy, and nonvisual (no camera). This application setting calls for new methods for activity recognition which can deal with the poverty and unreliability of the provided information, process streams of data, and whose models can be checked by human and linked to domain knowledge. To this end, we present a method based on Markov Logic Network (MLN) to recognise activities of daily living in a perceptive environment. MLN, a statistical relational method, makes it possible to build logical models that can deal with uncertainty. This method is detailed in Section 4. Before this, a state of the art in MLN based activity recognition is given in Section 2 and the Sweet-Home project is introduced in Section 3. The method was tested in an experiment in a real smart home involving more than 20 participants. The experiment and the results are described in Section 5. The paper ends with a discussion and gives a short outlook on further work.

State of the art of Human Activity Recognition in the home

(proposals) temporally labelled (e.g. : door slamming at 11 :32), signatures of specific situations of atomic events are detected through a process of hierarchical abstraction. For example, the movements detected in the bedroom can be part of the activity "get up" which itself can be part of a plan of the day (e.g ; : Sunday morning). Automatic recognition of activity is one of the most active and most ambitious research areas because of the large amount of noise in the data and the difficulty of modelling situations ; for the same person, an activity can take place in many ways.

Approaches for activity recognition can be divided mainly into three categories : statistical, probabilistic and logic. In the former category, machine learning methods have been applied to classify activities from information related to pervasive environments. For instance, Fleury et al. [START_REF] Fleury | SVM-based multi-modal classification of activities of daily living in health smart homes : Sensors, algorithms and first experimental results[END_REF] proposed Support Vector Machines (SVM) to implement a classifier using data from sensors in a real pervasive environment. If statistical methods such as SVM or Neural Networks can lead to good performance, they lack a formal base to represent uncertainty and the obtained models are not easily interpretable.

As information in pervasive environments is uncertain in most cases, probabilistic approaches are suitable candidates to be applied for activity recognition. For instance, Dynamic Bayesian networks were used by Van Kasteren et al. [START_REF] Van Kasteren | Bayesian activity recognition in residence for elders[END_REF] to recognise elders' activities. Considering the temporal nature of activities as a succession of actions or sub activities, literature presenting a modelling of activity by Hidden Markov Models (HMM) is vast. For instance, Duong et al. [START_REF] Duong | Efficient duration and hierarchical modeling for human activity recognition[END_REF] extended a conventional HMM to model the duration of an activity and Naaem et al. [START_REF] Naeem | Activity recognition using a hierarchical framework[END_REF] defined activities as a composition of tasks modelled by hierarchical HMMs. However, despite improved expressiveness, these models require a large amount of training data. These training data are costly to obtain and are often not generalisable to other settings than the one in which they were acquired. Moreover, it remains difficult to integrate a priori high-level knowledge in these probabilistic models.

The logical approach offers an ideal framework to model explicit knowledge. Ontologies have been used for this task [START_REF] Chen | Ontology-based activity recognition in intelligent pervasive environments[END_REF] since they feature readability and formal definitions while the activity recognition can be performed by an ontology reasoner as a problem of satisfiability. Moreover, under the logic approach, logic rules facilitate the implementation of expert knowledge within a model [START_REF] Storf | Rule-based activity recognition framework : Challenges, technique and learning[END_REF]. For instance, Augusto et al. [START_REF] Augusto | The use of temporal reasoning and management of complex events in smart homes[END_REF] used logical models to represent the temporal relations among events to recognise activities. The main drawback of this methods is the lack of systematic handling of uncertainty.

Recently, Statistical Relational Learning (SRL) [START_REF] Getoor | Introduction to Statistical Relational Learning[END_REF], a sub domain of machine learning, has gained much attention as it integrates elements of logic and probabilistic models. Under the SRL schema, models are defined in a formal logical language that makes them reusable and easy to verify, that systematically take uncertainty into account, and that allows easily inclusion of a priori knowledge. SRL has recently attracted attention in the domain of human activity modelling and recognition. For instance, Logic HMM and relational Markov networks are both SRL methods that were considered for activity recognition [START_REF] Natarajan | Logical hierarchical hidden markov models for modeling user activities[END_REF][START_REF] Liao | Location-based Activity Recognition[END_REF]. In our work we proposed to use Markov Logic Networks (MLN). To the best of our knowledge the closed approach to our is the one of Trans et al. [START_REF] Tran | Event modeling and recognition using markov logic networks[END_REF] who detected activities in video streams. Other MLN-based activity recognition methods were defined and tested under different settings from the Sweet-Home project. For instance, [START_REF] Helaoui | A statistical-relational activity recognition framework for ambient assisted living systems[END_REF] assumed RFID tags but this implies tagging every objects involved in the model and the practicability of the approach can be questioned. In our project, which is described in the next section input data imposes little constraint on the daily file of the user.

3 Sweet-Home : an Audio-Based Smart Home System

The Sweet-Home project (sweet-home.imag.fr) aims at designing a new smart home system based on audio technology focusing on three main aspects : to provide assistance via natural man-machine interaction (voice and tactile command), to ease social inclusion and to provide security reassurance by detecting situations of distress. If these aims are achieved, then the person will be able to pilot their environment at any time in the most natural way possible.

The input of the Sweet-Home system is composed of the information from the home automation system transmitted via a local network and information from the microphones transmitted through radio frequency channels. Rather than building communication buses and purpose designed material from scratch, the project tries to make use of already standardised technologies and applications. As emphasised in [START_REF] Edwards | At home with ubiquitous computing : Seven challenges[END_REF] the interoperability of ubiquitous computing elements is a well known challenge to address. Thus, the use of home automation standards ensure compatibility between devices, ease the maintenance and orient the smart home design toward cheaper solutions. While the home automation system provides symbolic information, raw audio signals must be processed to extract information from speech and sound. The extracted information is analysed and either the system reacts to an order given by the user or the system acts pro-actively by modifying the environment without an order (e.g. turns off the light when nobody is in the room). ù Output of the system thus includes home automation orders but also interaction with the user when a vocal order has not been well understood for example, or in case of alert messages (e.g. turn off the gas, remind the person of an appointment).

The Sweet-Home system will be piloted by an intelligent controller which will capture all streams of data, interpret them and execute the required actions. The diagram of this intelligent controller is depicted in Figure 1. All the knowledge of the controller is defined using two semantic layers : the low-level and the high-level ontologies. The former ontology is devoted to the representation of raw data and network information description while the high level ontology represents concepts being used at the reasoning level such as : Actions that can be performed in a home and the context in which a home can be (e.g., making coffee, being late). This separation between low and high levels makes possible a higher re-usability of the reasoning layer when the sensor network and the home must be adapted [START_REF] Klein | Ontology-centred design of an ambient middleware for assisted living : The case of soprano[END_REF]. The estimation of the current context is carried out through the collaboration of several processors, each one being specialised in a certain context aspect, such as location detection or activity recognition. All processors share the knowledge specified in both ontologies and use the same repository of facts. Furthermore, the access to the knowledge base is executed under a service oriented approach that allows any processor being registered to be notified only about particular events and saving any inferred information to be available to other processors. This data and knowledge centred approach permits to ensure that all the processors are using the same data structure and that the meaning of each piece of information is clearly defined among all of them. In addition, the chosen architecture is more flexible than a classical pipeline of processors, making possible the easy insertion of new processors. Once the current context has been determined, the controller evaluates if an action must be taken. What supports the process of decision is a set of logic rules which are part of the knowledge base.

Method

As shown in the previous section, activities is an important element of the context. In this study, the activities under consideration are daily living tasks such as sleeping, dressing, eating, communicating, etc. [START_REF] Katz | Assessing self-maintenance : activities of daily living, mobility, and instrumental activities of daily living[END_REF] that a person performs during a temporal interval. Given that the data streams provide quite poor, indirect (no wearable sensors) and sporadic (no continuous measurement of some variables) information as they are only composed of classical home automation sensors and microphones data ; fine grain activity recognition, such as screwdriver usage, is impracticable. However, each instance of activity is composed of a set of events that generate observations from the set of home automation sensors. Our hypothesis is that these set of observations are signatures of the activities and that they can be described by statistics of predefined variables computed over temporal windows shorter that the minimal activity duration. Although activities captured in this manner might be gross, we argue that they can be sufficient to provide contextual information to the decision module.

The method to recognise activities from the streams of raw sensor data goes through different levels of abstraction as depicted Figure 2. The raw data are composed of symbolic timestamped values (e.g., infra-red sensors), state values (e.g., switches), time series (e.g., temperature) and signals (e.g., microphones). A pre-processing stage extracts higher-level information such as speech, sounds, location and agitation of the inhabitant. To represent the stream of data, all the raw and abstracted data are summarised as attribute vectors, each of which corresponding to a temporal windows of size W . So, at current time t, every segment of the data of interval ]t -W, t] seconds is represented by a vector v(t) which is used as input to a classification model M which gives the main activity a of the person during ]t -W, t]. All of the classification models were acquired using supervised machine learning techniques. This section summarises the pre-processing stage, and details the attributes and the classifier model.

Preprocessing

The raw data captured within the smart home (see bottom of Fig. 2) contains information that must be extracted for enhanced activity recognition. Three types of abstraction are considered : localisation of the inhabitant -which is of primary importance for activity recognition -, speech and sound recognition -which is important for activities of communication -and activity levelwhich specifies how active the person was during the temporal window.

Speech/sound detection In this approach, sound events are detected in realtime by the AuditHIS system [START_REF] Vacher | In : Complete Sound and Speech Recognition System for Health Smart Homes : Application to the Recognition of Activities of Daily Living[END_REF]. Briefly, the audio events are detected in real-time by an adaptive threshold algorithm based on a wavelet analysis and an SNR (Signal-to-Noise Ratio) estimation. The events are then classified into speech or everyday life sound by a Gaussian Mixture Model. The microphones being omnidirectional, a sound can be recorded simultaneously by multiple microphones ; AuditHIS identifies these simultaneous events. Localisation In smart homes, cheap localisation can be performed by using infra-red sensors detecting movement but these sensors can lack sensitivity. To improve localisation, our approach fuses information coming from different data sources namely, infra-red sensors, door contacts and microphones. The data fusion model is composed of a two-level dynamic network [START_REF] Chahuara | Fusion of audio and temporal multimodal data by spreading activation for dweller localisation in a smart home[END_REF] whose nodes represent the different location hypotheses and whose edges represent the strength (i.e., certainty) of the relation between nodes. This method has demonstrated a correct localisation rate from 63% to 84% using several uncertain sources.

0 0 0 1 1 1 PIR 0 1 X X X X X X X X X X X X X X X X X X X X X X X

C°Temperature Hz Microphone

Audio

Activity Level In smart homes, the level of activity is a measure of the frequency of actions of the person in the house. This makes it possible to distinguish from activities that ask for many actions (e.g., cleaning the house) from quieter ones (e.g., sleeping). In our approach, level of activity is estimated not only from infra-red sensors but also from sound information as well as door contacts. These sources of data are fused using a linear model. Level of activity -which is a numerical measure-must not be confused with activity -which is the category of daily living activities being performed.

Generation of the Vectors of Attributes

The traces generated from human activities are difficult to generalise due to the high inter and intra-person variability of realisation of a task. This is why statistic attributes and inferred information were chosen to summarise the information present in each window. In total 69 attributes were extracted for each temporal window. They are summarised in Table 1. In addition to the set of attributes, the seven activities considered in the study are given at the end of the Table . It can be noticed that an unknown class is present. This class is composed of all windows during which none of the seven activities is being performed.

Markov Logic Network (MLN)

MLN [START_REF] Richardson | Markov logic networks[END_REF] combines first-order logic and Markov Networks. A MLN is composed of a set of first-order formulae each one associated to a weight that expresses a degree of truth. This approach soften the assumption that a logic formula can only be true or false. A formula that does not contain variables is ground and is a ground atom if it consists of a single predicate. A set of ground atoms is a possible world. All possible worlds in a MLN are true with a certain probability which depends on the number of formulae they satisfy and the weights of these formulae. A MLN, however, can also have hard constraints by giving a infinite weight to some formulae, so that worlds violating these formulae have zero probability. Let's consider F a set of first-order logic formulae, w i ∈ R the weight of the formula f i ∈ F , and C a set of constants. During the inference process, every MLN predicated is grounded and Markov network M F,C is constructed where each random variable corresponds to a ground atom. The obtained Markov network allows to estimate the probability of a possible world P (X = x) by the equation 1 :

P (X = x) = 1 Z exp fi∈F w i n i (x) (1)
where Z = x ′ ∈χ exp fi∈F w i n i (x ′ ) is a normalisation factor, χ the set of possible worlds, and n i (x) is the number of true groundings of the i-th clause in the possible world x. Exact inference in MLN is intractable in most cases, so Markov Chain Monte Carlo methods are applied [START_REF] Richardson | Markov logic networks[END_REF].

Learning an MLN consists of two independent tasks : structure learning and weight learning. Structure can be obtained by applying machine learning methods, such as Inductive Logic Programming, or rules written by human experts. Weight learning is an optimisation problem that requires learning data. The most applied algorithm in the literature is Scaled Conjugate Gradient [START_REF] Lowd | Efficient weight learning for markov logic networks[END_REF].

The approach we implemented uses a list or rules modelling the capacity of each feature value to discriminate an activity. Formally, this rules have the following structure f eature i (X, V i ) → class(X, V c ) where the variables X, V i , and V c represent : the temporal window to be classified, the value of the i th feature, and the value of the target class. Before creating the model, all numerical variables were discretised. In addition, the temporal relation between instances were modelled by means of the following rule previous(X, V c ) → class(X, V c ). The adequacy of including this rule comes from the fact that daily activities use to follow a certain pattern within the routine of an inhabitant. The weights for this model were learnt by Scaled Conjugate Gradient. Inference on test data is performed as though it was an on-line system. Thus, the classification of a temporal window not only considers the features describing it but also the results of the previous window classification.

Support Vector Machine

Support Vector Machine (SVM) [START_REF] Cortes | Support-vector networks[END_REF] is a classification and regression method. In essence, a SVM is a mathematical entity for maximizing a particular mathematical function with respect to a given collection of data (i.e. samples, measurements, records, patterns or observations). Similar to neural networks, SVMs possess the well-known ability of being universal approximators of any multivariate function. Consequently, they are of particular interest for modeling highly nonlinear complex systems. The simplest model of SVM is the so-called maximal margin classifier, which works only for data which are linearly separable in the feature space. However, SVM can be extended to treat nonlinear casesby the use of Kernel functions [START_REF] Cristianini | An Introduction to Support Vector Machines and Other Kernel-based Learning Methods[END_REF].

This method has already been used for activity recognition [START_REF] Fleury | SVM-based multi-modal classification of activities of daily living in health smart homes : Sensors, algorithms and first experimental results[END_REF] achieving acceptable rates of accuracy. That is why, we have chosen SVM as a baseline for our proposed model.

Experiments and results

The method was applied on data collected in a smart home during an experiment involving 21 persons. This section describes the pervasive environment in which the tests were performed (sec. 5.1), the data set (sec. 5.2) that was acquired and the results of the activity recognition (sec. 5.3).

Pervasive Environment

In the Sweet-Home project, the main pervasive environment considered is the Domus smart home depicted Figure 3. It was adapted to acquire realistic corpus and test the developed techniques. This smart home was set up by the Multicom team of the Laboratory of Informatics of Grenoble, partner of the project. It is a thirty square meters suite flat including a bathroom, a kitchen, a bedroom and a study, all equipped with sensors and effectors such as infrared presence detectors, contact sensors, video cameras (used only for annotation purpose), etc. In addition, seven microphones were set in the ceiling. The technical architecture of Domus is based on the KNX bus system 3 , a worldwide ISO standard (ISO/IEC 14543) for home and building control. Bus devices can either be sensors or actuators needed for the control of building equipments such as : lighting, shutters, security systems, energy management, heating, ventilation 3. www.knx.org and air-conditioning systems, interfaces to service and building control systems, remote control, metering, audio video control. . .Besides KNX, several field buses coexist in Domus, such as UPnP (Universal Plug and Play) for the audio video distribution, X2D for the opening detection (doors, windows, and cupboards), RFID for the interaction with tangible objects (not used in the Sweet-Home project). More than 150 sensors, actuators and information providers are managed in the flat. A residential gateway architecture has been designed, supported by a virtual KNX layer seen as an OSGI service (Open Services Gateway Initiative). This layer guarantees the interoperability of the data coming from the different field buses and allows the communication between them and towards virtual applications, such as activity tracking. More than 60 bundles delivering more than 60 services are running. Thanks to this gateway, all home automation elements as well as multimedia elements can be controlled and parametrised remotely.

The sensors that were used in the experiments were the following : -7 radio microphones set into the ceiling (2 per room except for the bathroom). These microphones are useful to detect communication activities, recognise speech or detect abnormal sounds ; -switches and door contact detectors connected to the KNX network which are useful for device usage (fridge, cupboard), informing about movement (e.g., door used between to rooms), knowing whether a window is open or a socket activated. -Two infra-red movement detectors connected to the KNX network ; -ambient sensors, such as temperature, humidity, CO 2 , etc. ; -electricity and water meters ; -video cameras only used to perform annotation of the data.

Experimental Data

An experiment was conducted to acquire a representative data set of activities performed at home. The Domus flat was designed to seem as normal as a standard flat (e.g., no visible wire, no prominent sensor) so that any participant's activity instance would be as close as possible to an instance performed in their usual manner. 21 persons (including 7 women) participated to the experiment to record all sensors data in a daily living context. The average age of the participants was 38.5 ± 13 years (22-63, min-max). To make sure that the data acquired would be as close as possible to real daily living, the participants were asked to perform several daily living activities in the smart home. A visit, before the experiment, was organised to make sure that the participants will find all the items necessary to perform the activities. No instruction was given to any participant about how they should behave. All the home automation data was recorded at the virtual KNX layer apart from video data which was recorded separately and audio data which was recorded in real-time thanks to a dedicated PC embedding an 8-channel input audio card [START_REF] Vacher | Development of audio sensing technology for ambient assisted living : Applications and challenges[END_REF].

The experiment consisted in following a scenario of activities without condition on the time spent and the manner of achieving them (having a breakfast, simulate a shower, get some sleep, clean up the flat using the vacuum, etc.). During this first phase, participants uttered 40 predefined casual sentences on the phone (e.g., "Allo", "J'ai eu du mal à dormir") but were also free to utter any sentence they wanted (some did speak to themselves aloud). At the end, more than 26 hours of data were recorded. All the activities as well as other information such as location, position, etc. were annotated using the advene software 4 .

The stream of data was analysed window by window to generate 2122 instances described by the 69 attributes detailed in Section 4.2. The temporal window size was chosen empirically to be 1 minute. Moreover, given that some activities might intersect with several windows, a 25% overlap was applied. This gives an on-line system that recognises activities every 45 seconds.

Results

The MLN approach was applied to the experimental data collected in the smart home. In order to assess improvement, we also applied a Naive Bayes (NB) classifier known to be simplistic but often efficient and a more elaborate approach based on Support Vector Machine (SVM) which showed very good results on a similar task [START_REF] Fleury | SVM-based multi-modal classification of activities of daily living in health smart homes : Sensors, algorithms and first experimental results[END_REF]. These two classifiers NB and SVM provide the baseline results. The learning and testing strategy used was leave-one-out which consisted in learning models successively on 20 participants and testing on the remaining one. The results on the 21 combinations are then averaged to give the overall performance.

Table 2 shows the precision and recall for the methods. The overall accuracy achieved with MLN, 85.3%, is significantly higher than the one obtained with SVM, 59.6% and Naive Bayes, 66.1% . The unknown class case, which corresponds to temporal windows that have not been labelled, exhibits the lowest performance due to the fact that none of the methods can characterise the class. These unlabelled windows can, indeed, take place in very different circumstances, mainly within the transition of two activities, what makes difficult to model them. When the Unknown class is excluded from the data set the overall performances significantly increase showing again the very good performance of MLN (acc. = 90.5%).

We believe that, in spite of its simplicity, our MLN model is well suited for activity modelling and classification because it covers exhaustively all the possible relations among sensors and activities. Even more, in this particular case it seems sound to assume that a sensor evidence about an activity being performed is independent of the other sensors information given the activity. Consequently, our model gives very acceptable results relying mostly in rules modelling independently the influence of a sensor value to recognise an activity. We show below some of the rules composing the MLN model having the highest weights after the process of weight learning : This subset of rules characterises the implicit knowledge learnt by the model. Many of the rules having a high weight are concerned with location of the inhabitant, what is easily explained by the fact that most activities are performed in specific rooms. Indeed, several previous studies highlighted the importance of location for activity recognition. However, other information appropriately complement location, as in the above example a medium electricity consumption helps to detect the vacuum cleaner usage and consequently the tidying up activity.

Table 3 shows the confusion matrix for the recognition with MLN taking the unknown class into account. The matrix exhibits high values in the confusion of eating and tidying up since they are often performed in the same location (tidying up is also preformed in the bedroom) and complementary information are similar in some occasions : water consumption, sounds, opening of placard doors. Moreover, the confusion of these two activities represents the main difference in accuracy results among SVM and MLN. In general, confusion is higher when activities share a common location as : Tidying up/sleeping and Tidying up/resting. From these results we can conclude that MLN models better the complementary information to discriminate activities performed under similar settings. Actually, the set of learnt rules in our MLN model characterises any detail of a sensor value that can be useful to recognise an activity. Additionally, note that a weighted set of logic rules is a good model to represent knowledge. Being highly readable and clear, its analysis can help to understand core differences between sensor information related to activities in pervasive environments. It also can be noticed that the use of microphones, which is an essential feature of the Sweet-Home project, proved to be very important for activity recognition. Indeed, detection of speech is fundamental to recognise communication activity. This explains the high accuracy of this activity shown in the confusion matrix. Sound plays also an important role ; for instance, the amount of sound in the bedroom can resolve the ambiguity between dressing up and sleeping, which are both performed in the same location.

An important finding drawn from these results is that SVM and Naive bayes models are more easily affected by the unbalanced number of instances. Thus, MLN performs better on classification of classes having few instances such as dressing up and hygiene. In real daily routines, some activities have a short duration and are carried out just a few times, then the capacity of MLN to deal with unbalanced training data seems appropriate to be applied in smart homes. 6 Discussion and perspective

The findings of our study allow us to assert that MLN based models have features that make them more adapted than traditional classifiers for activity recognition. The main advantages of the presented MLN model are : the completeness to represent every detail of sensor values and activity relations ; the readability of the model to understand which sensors explain better the occurrence of an activity ; the possibility of including additional knowledge to the model through logic rules, as it was done with the temporal relations among instances ; and the ability to learn from unbalanced data sets.

Another great advantage of MLN rely on its formal logic nature. In Ambient Intelligent systems, the domain knowledge is often represented as logic formulae (e.g., Description Logic in the case of the OWL format). When possible, this permits translation from one representation to another to performs, for instance, consistency checking of MLN models or addition of relational knowledge as a priory knowledge in the MLN structure learning. In this perspective, the use of a formal domain knowledge description and logic-based recognition method could leads to a higher re-usability of the model learnt in one home to another home. Given the difficulty and cost of acquiring training data in the smart home domain this way seems promising to alleviate the need of large volumes of training data of purely statistical methods.

On the uncertainty modelling, the MLN being a probabilistic model, the outputs of the MLN inference can be exploited and fused with other uncertain evidence in the context-aware decision as it is the case in the intelligent controller described in Section 3. This ability might be highly interesting in other challenging application such as recognition of interleaving activities. In addition, we believe that some characteristics of MLN for activity recognition go beyond the mere classification. Thus, the analysis of set of logic rules composing the MLN and their weights can give us rich information to be exploited during the design of the Sweet-Home context aware system.

Figure 1 .

 1 Figure 1. The Intelligent Controller Diagram

4 PROCESSINGFigure 2 .

 42 Figure 2. Temporal windowing for computing the vectors from the sensors data.

Figure 3 .

 3 Figure 3. The Domus Smart Home

4 .

 4 liris.cnrs.fr/advene/

Table 1 .

 1 Attributes used for activity recognition (all the attributes are numerical)

	Attributes	Number comments
	PourcentageLoc x	4	ratio of time spent at room x
	PredominantLoc	1	most occupied room during the temporal window
	LastRoomBeforeWindow	1	last room in which the person was just before the
			current window
	TimeSinceInThisRoom	1	Time elapsed since the person entered the room
	ActivationDeactivationWindow y	6	number of state changes of the door contact of the
			window y
	ActivationDeactivationDoor w	4	number of state changes of the door contact of the
			door w
	ActivationDeactivationLight z	6	number of state changes of the light z
	ActivationDeactivationCommDoor f	5	number of state changes of the door contact of the
			furniture f
	DetectionPIR x	2	number of time the movement detector fired in
			room x
	AmbientSensor	13	difference of value between temporal windows of :
			CO2, temperature, humidity, brightness, water
			and electricity
	Power LastUse	3	Id of the last used sockets or switches.
	PercentageTime Sound	1	ratio of time occupied by sounds during the tem-
			poral window
	PercentageTime Speech	1	ratio of time occupied by speech during the tem-
			poral window
	sound m	7	number of sound occurrences detected by micro-
			phone m
	speech m	7	number of speech occurrences detected by micro-
			phone m
	PercentageAgitation	6	number of events per windows for the category :
			room, doors, electricity, water, sounds and speech
	TotalAgitation	1	sum of the PercentageAgitation in the temporal
			window
	Class	1	eating, tidying up, eliminating, communicating,
			dressing up, sleeping, resting, unknown

Table 2 .

 2 Overall Accuracy, precision and recall

	Method	SVM		Naive Bayes	MLN
	Accuracy	59.64		66.1		85.25
		Precision	Recall	Precision	Recall	Precision	Recall
	Eating	64.8	71.0	75.1	79.8	90.4	91.9
	Tiding Up	40.0	39.0	58.3	56.4	75.1	86.9
	Hygiene	55.8	57.4	67.4	61.7	82.6	80.9
	Communicating	83.7	71.9	40.9	47.4	100.0	82.5
	Dressing Up	32.3	41.1	13.3	11.8	85.3	56.9
	Sleeping	57.6	60.1	60.1	74.3	84.7	82.2
	Resting	81.5	73.5	82.4	70.8	90.2	92.2
	Unknown	10,2	8.2	19.7	17.9	63.6	25.0
	2.17 : P ercentageLocationBedroom(win, High) => class(win, Sleeping)
	2.14 : P ercentageAgitationElectricity(win, M edium) => class(win, T idyingU p)
	1.94 : SpeechStudy(win, High) => class(win, Communication)
	1.85 : SoundBedroomM ic1(win, M edium) => class(win, Dressing)

Table 3 .

 3 Confusion Matrix for MLN results with Unknown class)

	True class/Prediction	1	2	3	4	5	6	7	8
	Eating(1)	546	47	0	0	0	1	0	0
	Tiding Up(2)	23	373	3	0	1	18	4	7
	Hygiene(3)	14	6	114	0	2	0	5	0
	Communicating(4)	0	2	0	47	0	0	8	0
	Dressing Up(5)	2	8	6	0	29	1	5	0
	Sleeping(6)	17	9	11	0	0	221	11	0
	Resting(7)	0	22	0	0	1	9	458	5
	Unknown(8)	2	30	4	0	1	11	17	21

⋆. This work is part of the Sweet-Home project founded by the French National Research Agency (Agence Nationale de la Recherche / ANR-09-VERS-011)


X Artru
email: x.artru@ipnl.in2p3.fr

E Redouane-Salah

COLLINS ASYMMETRY IN FIELD IONIZATION OF HYDROGEN 1

An effect similar to the Collins asymmetry is found in the ionization of a hydrogen atom by a static electric field E. When the initial electron possesses an orbital angular momentum L transverse to the field, the mean transverse velocity v T of the final electron points in the direction of E × L . However L is oscillating in time due to the linear Stark effect, making v T oscillate.

Introduction. An atom can be ionized by a sufficiently strong static electric field E thanks to the tunnel effect. This process has a strong similarity with the production of a quark-antiquark pair (q q) in a QCD string. If the initial electron has an orbital angular momentum perpendicular to E, the average transverse velocity v T should be nonzero and in the direction of L × F, where F = -eE is the external force [1]. We refer to it as the v.(L×F) asymmetry. The mechanism(Fig. 1-left) looks like the string + 3 P 0 mechanism (Fig. 1-right) of hyperon polarization [2] and Collins effect [1,3].

At variance with the string + 3 P 0 mechanism, the Schwinger mechanism of q q pair creation yields no v.(L×F) asymmetry [1]. Thus the question of such an asymmetry in string breaking remains open. It is at least instructive to study it in atomic physics.

Behavior of an H atom in an external electric field

We consider an hydrogen atom in an static electric field E = -(F/e) ẑ. At small F the linear Stark effect just splits the n th energy level in 2n -1 sublevels separated by 2 ω = 3nF/2. Stark states are the eigenstates of H 0 -F z = p 2 /2 -1/r -F z in the F → 0 limit. For large enough F ionization by tunneling becomes important and Stark states move into resonances of complex energy E = E R -iγ/2. Using the parabolic coordinates ξ=r-z, η=r+z, ϕ=arg(x + iy), their wave functions have the separable form [START_REF] Landau | Course of theoretical physics[END_REF]

Ψ = ξ -1/2 Φ(ξ) η -1/2 χ(η) e imϕ (1)
where Φ(ξ) verifies L ⊥ oscillations. Stark states are also eigenstates of A z , where A is the Laplace-Runge-Lenz-Pauli vector

∂ 2 Φ/∂ξ 2 + E/2 + Z ξ /ξ -(m 2 -1)/(4ξ 2 ) -F ξ/4 Φ(ξ) = 0 . (2
A = r/r + (L × p -p × L)/2 . (3)
For F =0, A z =2 z /(3n 2 ) = (n η -n ξ )/n. For F = 0 the transverse components (L x , L y ) and (A x , A y ) are not conserved. Starting from a L y eigenstate, L y oscillates in quadrature with A x , as pictured in Fig. 2, with the period 2π/ω. Let us take as an example the initial state |n = 2, L y = +1 , whose wave function is

Ψ(r, t = 0) = 8 -1 π -1/2 (z + ix) e -r/2 = 0.5( |010 -|100 + i|001 + i|00 -1 ) . (4)
At t = 0 it evolves as

Ψ(t) = 0.5 e it/8 e +iωt |010 -e -iωt |100 + i|001 + i|00 -1 (5) = e it/8 cos 2 ωt 2 |L y = +1 -sin 2 ωt 2 |L y = -1 + i √ 2 sin(ωt)|l = 0 . (6)
Thus the atom oscillates between three L y eigenstates.

time The external force is confining in ξ and changes Φ(ξ) only little. Tunneling bears on χ(η). The wave function at large η describes the escaped electron. Using, as in Ref. [START_REF] Landau | Course of theoretical physics[END_REF], the JWKB method to lowest order in F , one obtains for the state |i ≡ |n ξ , n η , m

Ψ i (r, t) η→∞ ≃ a i Φi (x, ŷ) exp{(-iδE i -γ i /2)t ′ } B(η, t) . ( 7
)
a i is the tunneling amplitude normalized to |a i | 2 = γ i , δE i is the Stark shift, Φi (x, ŷ) is the 2-D oscillator wave function normalized to Φi | Φi = 1 and

B(η, t) = (4F η 3 ) -1/4 exp (i/3) √ F (η -η F ) 3/2 + it/8 + 5iπ/4 . ( 8
)
η F ≡ 1/(n 2 F
) is near the tunnel exit and t ′ ≡ t -(η -η F )/F is the classical electron exit time. For n=2 the amplitudes are

a 1 ≡ a 010 = iq a 00+1 , a 2 ≡ a 00+1 = a 00-1 = 2 -5/2 F -1 exp [-1/(24F )] , a 3 ≡ a 100 = a 00+1 /(iq) , (9)
with q = e -3/2 / √ 2F . The widths γ i = |a i | 2 agree with Slavjanov's result [START_REF] Yu | Problemi Matematicheskoi Fiziki[END_REF].

3 v.(L×F) asymmetry for the initial state |n = 2, L y = +1

With the initial state (4) the escaped electron density is, according to (

,

|Ψ(r, t)| 2 η→∞ = (4F η 3 ) -1/2 Φ(x, ŷ, t ′ ) 2 (10)
with η ≃ 2z, (x, ŷ) ≃ (x, y)/ √ 2nz. In the n=2 case,

Φ(t ′ ) = 0.5 a 1 Φ010 e (iω-γ 1 /2)t ′ -a 3 Φ100 e (-iω-γ 3 /2)t ′ + ia 2 ( Φ00+1 + Φ00-1 ) e -γ 2 t ′ /2 . ( 11
)
|Ψ(r, t)| 2 looks like the density of a classical electron cloud falling freely in the force field F. An electron leaving the tunnel at time t ′ with the transverse velocity v ⊥ follows the parabola of fixed (x, ŷ) ≃ v ⊥ / √ 2F . The interference between even-and odd-m terms of Φ(t ′ ) yields the v.(L×F) asymmetry, which is t ′ -dependent. A measure of it is

A(t ′ ) ≡ v x /∆v x = Φ(t ′ )|x| Φ(t ′ ) / Φ(t ′ )|x 2 | Φ(t ′ ) ; (12)
A(t ′ = 0) = 8 1/2 q 2 + 8 + 3 q -2 -1/2 . ( 13
)
Like L y , A(t ′ ) changes sign at the Stark frequency, giving the "crawling snake" of Fig.

3 [START_REF] Redouane-Salah | AIP Conf. Proc[END_REF].

Conclusion.

This study shows that the v.(L×F) effect does exist in field ionisation, but is oscillating in time. Several constraints make its search challenging:

• Radiative transition may compete with field ionization.

• The initial asymmetry A(0) is small if the |a i |'s differ too much (see Eqs.13 and 9). • A(t ′ ) is fast oscillating, therefore one may only measure its time-averaged A . This one is large only if γ i ω, so that ionization is faster than oscillation.

These constraints are satisfied with a large enough field. In the n=2 case this field is too strong to be produced in laboratory. Hopefully, our results can be generalized to large n (Rydberg states), where the required field scales like n -4 [START_REF] Artru | [END_REF]. The v T distribution can be measured by the photoelectron imaging techniques [START_REF] Yu | [END_REF]9].

Our formulae, obtained at lowest order in F , cannot be applied at the required field. Accurate numerical methods are given in [10,11]. Nevertheless the above conclusions should remain qualitatively correct.

Figure 1 :

 1 Figure1: Left: semi-classical motion of the electron extracted form the hydrogen atom by a strong field E, when the electron is initally in a L y = +1 state. Right: String + 3 P 0 mechanism correlating the tranverse momentum and the transverse polarization of a quark created in string decay[1,3].

Figure 2 :

 2 Figure 2: Classical picture of the Stark oscillations of L y and A x .

  atom

Figure 3 :

 3 Figure 3: "Crawling snake" motion of x versus z of the escaping electron. As t grows the undulations move to the right.

Presented at XVI Advanced Research Workshop on High Energy Spin Physics (DSPIN-13)(Dubna, October 8-12,

2013)2 In this paper we use atomic units: /(m e αc) = 0.0529 nm for length, /(m e α 2 c 2 ) = 2.42 10 -17 s for time, m e α 2 c 2 = 27, 2 eV for energy and m 2 e α 3 c 2 / = 5.14 10 9 eV/cm for force.


Muhammad Usman
email: muhammad.usman@uaf.edu.pk

Sébastien Martin

Nicolas Cimetiere

Sylvain Giraudet

Vincent Chatain

Khalil Hanna

N Cimetière

Sorption of nalidixic acid onto micrometric and nanometric magnetites: experimental study and modeling

Keywords: magnetite, nalidixic acid, sorption, transport, column, modeling

Introduction

In environment, iron minerals are commonly found as ferric oxides including goethite, ferrihydrite, hematite and lepidocrocite [START_REF] Schwertmann | Iron Oxides in the Laboratory: Preparation and Characterization[END_REF] . Another form of iron minerals is the mixed Fe II -Fe III oxides including magnetite (Fe 3 O 4 ) and green rust. Magnetite (Fe II Fe III 2 O 4 ) is very efficient in environmental remediation owing to its stability and presence of structural Fe II [START_REF] Usman | Remediation of PAH-contaminated soils by magnetite catalyzed Fenton-like oxidation[END_REF][START_REF] Usman | Treatment of hydrocarbon contamination under flow through conditions by using magnetite catalyzed chemical oxidation[END_REF][START_REF] Sposito | The chemistry of soils[END_REF][START_REF] Xue | Adsorption and oxidation of PCP on the surface of magnetite: Kinetic experiments and spectroscopic investigations[END_REF]. Magnetite is a ubiquitous iron oxide in soils and sediments. Existence of magnetite was reported in weathered clays, soils and in recent deposits of marine and freshwater sediments [START_REF] Karlin | Authigenic magnetite formation in suboxic marine sediments[END_REF][START_REF] Maher | Formation of ultrafine-grained magnetite in soils[END_REF]. Recently, magnetite was identified as the main constituent of iron corrosion scale in drinking water distribution systems [START_REF] Peng | Characterization of elemental and structural composition of corrosion scales and deposits formed in drinking water distribution systems[END_REF]. Top layers of corrosion scale were dominated by magnetite [START_REF] Peng | Characterization of elemental and structural composition of corrosion scales and deposits formed in drinking water distribution systems[END_REF][START_REF] Sarin | Physico-chemical characteristics of corrosion scales in old iron pipes[END_REF]. Magnetite can also be formed in laboratory by various abiotic and biotic procedures.

Formation of biogenic magnetite was reported as a result of microbial reduction of ferric oxyhydroxides [START_REF] Zegeye | In situ monitoring of lepidocrocite bioreduction and magnetite formation by reflection Mossbauer spectroscopy[END_REF]. Abiotic procedures to form magnetite include co-precipitation of Fe II and Fe III salts in aqueous solutions or partial oxidation of hydroxylated Fe II solution [START_REF] Ruby | Synthesis and transformation of iron-based layered double hydroxides[END_REF].

Magnetite can also be formed by reacting aqueous Fe II with ferric oxides inducing their structural modifications and bulk phase transformations [START_REF] Usman | FeII induced mineralogical transformations of ferric oxyhydroxides into magnetite of variable stoichiometry and morphology[END_REF][START_REF] Usman | Transformation of various kinds of goethite into magnetite: Effect of chemical and surface properties[END_REF]. The morphology, crystallography and specific surface area of natural or synthetic magnetite can vary widely.

Magnetite exists as micrometric and nanometric particles in many natural and engineered environments. Because of the larger specific surface area of nanosized particles, their surface reactivity is exalted and they play preeminent role in sorption of environmental pollutants.

Many studies have been carried out to evaluate the magnetite adsorption capacity for different pollutants including heavy metals, oxyanions and radionuclides [START_REF] Chowdhury | Arsenic and chromium removal by mixed magnetitemaghemite nanoparticles and the effect of phosphate on removal[END_REF][START_REF] Martínez | Sorption of selenium(IV) and selenium(VI) onto magnetite[END_REF][START_REF] Dixit | Comparison of Arsenic(V) and Arsenic(III) Sorption onto Iron Oxide Minerals: Implications for Arsenic Mobility[END_REF][START_REF] Missana | Uranium (VI) sorption on colloidal magnetite under anoxic environment: experimental study and surface complexation modelling[END_REF][START_REF] Missana | Selenite retention by nanocrystalline magnetite: Role of adsorption, reduction and dissolution/coprecipitation processes[END_REF]. However, less information is available about the mechanism and extent of sorption of emerging organic contaminants especially pharmaceutical compounds. Therefore, it is important to consider the potential mobilization risks of water pollution associated with these contaminants, and to investigate their interaction with magnetite.

Although large variability of magnetite is found in natural as well as engineered systems, sorption onto different magnetites has never been reported.. The impact of particle size and morphology on magnetite sorption capability merits, therefore, to be investigated form both environmental and engineering aspects. Moreover, the interactions of environmental pollutants with magnetite were mainly investigated under batch conditions [START_REF] Dixit | Comparison of Arsenic(V) and Arsenic(III) Sorption onto Iron Oxide Minerals: Implications for Arsenic Mobility[END_REF][START_REF] Missana | Uranium (VI) sorption on colloidal magnetite under anoxic environment: experimental study and surface complexation modelling[END_REF][START_REF] Missana | Selenite retention by nanocrystalline magnetite: Role of adsorption, reduction and dissolution/coprecipitation processes[END_REF]; however transport of such contaminants in magnetite-packed column has scarcely been investigated under flow-through conditions. Contrary to batch tests, column experiments allow monitoring the effect of non-equilibrium sorption onto the transport of pollutants. Effect of hydrodynamic parameters (e.g. dispersion) on the solute breakthrough can also be evaluated in continuous flow through conditions. Estimation of field parameters could be more accurate in column tests which provide a suitable soil-aqueous phase ratio. Moreover, sorbate species can be flushed out of system in continuous flow conditions, ultimately affecting the kinetics and extent of reaction.

Present study was conducted to investigate sorption of NA (used as a model pharmaceutical pollutant), onto three kinds of magnetite. Sorption was evaluated vs. time, pH and ionic strength in batch experiments. Sorption isotherms were also recorded over a wide range of NA concentration. Fourier transform infrared in transmission mode (FTIR) was also used to recognize the main surface complexes structures. Flow through experiments were also conducted at two influent concentrations (50 and 200 µM of NA) and at a relatively lower flow rate (i.e. 0.2 mL/min). Three different models (Thomas, Yan and Yoon-Nelson) were used to estimate the amount of NA sorbed in the column. Application of these semi-empirical models to determine the sorbed quantity of emerging organic pollutants in iron-mineral coated sand columns remains sparse.

Experimental Procedures

Formation and characterization of magnetite (M) and magnetite coated sand (MCS)

Experiments were conducted with three different kinds of magnetite (Fe II Fe III 2 O 4 ). Among them, two (M1 and M2) were prepared in lab, while third one (M3) was purchased from Prolabo. M1 and M2 were formed by mineralogical transformations of 2-line ferrihydrite and lepidocrocite (γ-FeOOH), respectively as previously reported [START_REF] Usman | FeII induced mineralogical transformations of ferric oxyhydroxides into magnetite of variable stoichiometry and morphology[END_REF]. Prior to reactivity tests, all magnetites were analyzed by X-ray powder diffraction (XRD), Transmission electron microscopy (TEM) and Fourier transform infrared spectrometer (FTIR) as described previously [START_REF] Usman | Remediation of PAH-contaminated soils by magnetite catalyzed Fenton-like oxidation[END_REF].

Magnetite coated sand (MCS) was prepared as described by Scheiddeger et al. [START_REF] Scheidegger | Coating of silica sand with goethite: preparation and analytical identification[END_REF] and as explained previously [START_REF] Hanna | Adsorption of aromatic carboxylate compounds on the surface of synthesized iron oxide-coated sands[END_REF][START_REF] Tanis | Experimental and modeling studies of sorption of tetracycline onto iron oxides-coated quartz[END_REF] by using 1 g of each magnetite per 100 g of sand (1% w/w).

Mineral characterization of sand was found to be exclusively quartz by XRD.

Sorption experiments

Batch tests

Kinetic sorption was evaluated at 200 µM of NA concentration, at a fixed pH (6.5) and ionic strength (NaCl 10 -2 M) and at 20 °C in the absence of light. The sorption isotherms were recorded at pH of 6.5 and wide range of NA concentration (2-200 µM). The sorption edge experiments were performed at a fixed NA concentration (50 µM) and ionic strength (NaCl 10 -2 M). Suspensions were centrifuged, filtered and the filtrate samples were subjected to analyses by UV-visible spectroscopy and depletion method was used to calculate the sorbed concentrations. Negligible quantity of dissolved Fe was detected by colorimetric method. The sorption tests are detailed previously [START_REF] Hanna | Reactive transport of gentisic acid in a hematite-coated sand column: Experimental study and modeling[END_REF][START_REF] Clervil | Sorption of nalidixic acid onto sediments under batch and dynamic flow conditions[END_REF].

To investigate the effects of ionic strength and that of phosphate, batch sorption experiments were carried out at various molar concentrations (10 -4 -10 -1 M) of NaCl, and of phosphate (10 -5 -10 -2 M). In order to determine the mass balance, solid phase extraction was conducted using acetonitrile as an organic solvent.

The sorption tests were performed in triplicate and their standard deviation was found to be less than 5%.

Column experiments

Dry MCS (50 g) was packed into glass columns having internal diameter of 2.6 cm providing bed length of 6.3 cm and bulk density of 1.49 g/cm 3 . Each column contained 0.5 g of the reactive material, i.e. magnetite.

The column was then saturated with a 10 -2 mol L -1 NaCl solution at a fixed flow rate (0.2 mL/min; q =0.037 cm/min). The hydrodynamic parameters were determined by a bromide tracer experiment (using a 10 -2 mol L -1 KBr solution) and using classical Convection Dispersion Equation (CDE) as explained previously [START_REF] Hanna | Reactive transport of gentisic acid in a hematite-coated sand column: Experimental study and modeling[END_REF][START_REF] Rusch | Sorption and Transport of Salicylate in a Porous Heterogeneous Medium of Silica Quartz and Goethite[END_REF][START_REF] Hanna | Transport of two naphthoic acids and salicylic acid in soil: Experimental study and empirical modeling[END_REF]:

x C v x C D t C         2 2 (1)
where c is the water solute concentration (M/L 3 ), t denotes time (T), x is the spatial coordinate (L), D represents the dispersion coefficient (L 2 /T), q is the flow velocity (L.T -1 ), θ is the volumetric water content (L 3 /L 3 ), and v is the darcian velocity = q/θ (L.T -1 ). The breakthrough curve of bromide exhibited a slight asymmetrical shape with little tailing (data is not presented). The bromide concentration was analyzed using CDE to estimate the values of  and D which represents flow homogeneity, as explained previously [START_REF] Clervil | Sorption of nalidixic acid onto sediments under batch and dynamic flow conditions[END_REF][START_REF] Hanna | Transport of two naphthoic acids and salicylic acid in soil: Experimental study and empirical modeling[END_REF][START_REF] Hanna | Sorption of two naphthoic acids to goethite surface under flow through conditions[END_REF]. NA solution (200 µM, pH = 6) was then injected in a continuous mode into the column at the same constant flow rate (0.2 mL min -1 ), under O 2 -free controlled atmosphere.

Results and discussion

Characterization of tested magnetites

Three kinds of magnetite were analyzed by XRD and their diffractograms are shown in Figure 1a. Five different peaks are represented in XRD diffractograms at 2 = 21.2 , 35 , 41.2°, 50.4° and 62.8° which could be assigned to magnetite in all diffractograms. These main peaks have d-space values of 2.53, 2.96, 2.09, 4.85 and 1.71 Å which may correspond to the more intense lines 311, 220, 400, 111 and 422, respectively of magnetite.

Morphology of three kinds of magnetite is shown by TEM images (Fig. 1b). M1 is characterized by smaller particles with non-uniform size or shape. But, shape of M2 particles is between hexagonal to octahedral while M3 exhibits non-uniform size and shape. Particle size of tested magnetites was in following order; M1 < M2 < M3 while a reverse order was found for BET surface area (M1 > M2 > M3) (Table 1). If particles are considered to be spherical, the radius of these particles (ρ = 5.15 x10 6 g m -3 ) could be correlated to the surface area as SSA Geo = 6/(ρd). A good agreement between SSA determined by BET and SSA Geo was observed except for M1. The disagreement observed for M1 might be caused by the existence of particles with wide range of particle size, and/or some impurities like ferrihydrite remaining during synthesis. Point of zero charge (PZC) determined by potentiometric titration was similar to that described in literature (Table 1) [START_REF] Xue | Adsorption and oxidation of PCP on the surface of magnetite: Kinetic experiments and spectroscopic investigations[END_REF].

Sun and co-workers [START_REF] Sun | Surface Characteristics of Magnetite in Aqueous Suspension[END_REF] proposed an approximation to determine the theoretical maximum surface proton binding site concentration (P s ) (mol L -1 ) using the following expression:

3 / 2 . . . . v N N Z A S P A S s  (2)
Where S represents the concentration of solid (0.5 g/L), A is the specific surface area, Z represents the number of formula units/unit cell (8 for magnetite), Ns denotes average number of protons per unit surface (it is assumed that proton is bounded at three hydrated surface iron sites), N A is Avogadro's number, and ν is cell volume of magnetite (5.91x10 -28 cm 3 ). These estimated values (Table 1) were, however, considerably higher than those of the concentration of surface proton binding sites obtained by potentiometric titrations. These observations are similar to those of Sun and co-workers [START_REF] Sun | Surface Characteristics of Magnetite in Aqueous Suspension[END_REF], which suggest that only a small part of ironsurface site seems to be involved in proton binding.

Batch sorption results

Kinetic results:

The sorption kinetics of NA showed that solute uptake reached equilibrium values at about 500 min for all solids (Fig. 2a). Various models namely pseudo-first-order, pseudo-second-order and intraparticle diffusion models were employed in order to evaluate the kinetic sorption mechanism. First-order and intraparticle diffusion models result in poor regression (r 2 ) of coefficient (data not shown). However, the pseudo-second-order rate expression appears to provide the best fitting kinetic model for the experimental data. The equation of pseudo-second-order can be expressed as:

dt dq = 2 2 ) ( t e q q k  (3)
where k 2 (g µmol -1 min -1 ) is the pseudo-second-order rate constant, q e is the amount of NA adsorbed at equilibrium (µmol g -1 ) and q t is the amount of the adsorption (µmol g -1 ) at any time t. Integration and rearrangement of Equation ( 4) gives:

t q t = t q q k e e 1 1 2 2  (4)
Pseudo-second-order rate constants (k 2 and q e ) were calculated from the slope and intercept of the plots of t/q t vs. t. The value of the constant k 2 determined by regression analysis are reported in Table 2. Kinetics of NA sorption followed the pseudo-second-order model, which suggests that chemisorption could be the adsorption rate-limiting step and NA adsorption occurs probably via surface complexation reactions at specific sorption sites.

It is generally known, the longer the compound is adsorbed on the surface, the stronger is its binding [START_REF] Chiou | A Physical Concept of Soil-Water Equilibria for Nonionic Organic Compounds[END_REF]. Thus, in present batch tests, M1 showed highest sorption extent and lowest sorption rate constant normalized per mass unit. However, this trend is modified and the constant rates values are closer to each other, when normalized to surface area.

Mass transfer rates were estimated to evaluate the potential role of diffusion, either stationary layer diffusion from the solution to the surface, or inter-particle pore diffusion to reach the sorption sites within the magnetite aggregates. The rate of diffusion α can be written as:

2 L D   (5)
where D is the diffusion coefficient (cm 2 /s), and L is the thickness of the stagnant liquid film (cm).

Diffusion coefficient of solutes is usually ~10 -9 m 2 /s in liquids and thickness of stagnant layer of the liquid film can be estimated by film theory as ~10 -6 m [START_REF] Sherwood | Mass Transfer[END_REF]. Therefore, mass transfer rate of solute through the liquid film by diffusion (external mass transfer resistance) and the rate of diffusion are estimated to 10 -3 m/s and to 10 3 s -1 respectively. Length of diffusion in nano-particle aggregates must be considered to assess the pore diffusion rate (resistance of internal mass transfer). Average size of aggregate could be roughly estimated by considering it as the average pore length for the particles of tested magnetite, and it lies at ~10 -6 m. The effective diffusivity of solutes in the pores is generally ~10 -10 m 2 /s [START_REF] Levenspiel | Chemical Reaction Engineering[END_REF]. Therefore, the internal mass transfer and the internal diffusion rate are estimated at 10 -4 m/s and 10 2 s -1 , respectively.

Rate of NA sorption onto magnetite was assessed from the kinetic data and maximum sorbed amount (k 2 .qe (s -1 )) varied between 5.1 10 -4 (M1), 1.5 10 -3 s -1 (M2) and 6.0 10 -3 s -1 (M3). Thus, the diffusion rate to the surface via external film or through the internal pores is much rapid than the NA sorption rate onto the magnetite surface. Thus, the intrinsic chemical reactions on the surface of iron oxide are likely to be the rate-limiting step.

Interparticle diffusion in NA sorption was determined experimentally by ultrasonic mixing which was employed to disperse loosely formed aggregates in the aqueous phase. In this case, the sorption rate should be faster if the interparticle diffusion is the rate-controlling step [START_REF] Hanna | Reactive transport of gentisic acid in a hematite-coated sand column: Experimental study and modeling[END_REF][START_REF] Hanna | Transport of two naphthoic acids and salicylic acid in soil: Experimental study and empirical modeling[END_REF][START_REF] Hanna | Surface Complexation of 2,5-Dihydroxybenzoic Acid (Gentisic Acid) at the Nanosized Hematite-Water Interface: An ATR-FTIR Study and Modeling Approach[END_REF]. Sorption data with ultrasonication is in agreement with that of magnetic stirring which suggests that interparticle diffusion is not the rate-limiting step. Mass balance on solidand aqueous-phase NA was determined in every case which suggests that NA was removed only by sorption and not by molecular transformation or other phenomena.

Effect of initial concentration and solution chemistry on NA sorption: Sorption isotherms were determined and fitted to the Langmuir, Freundlich and Tempkin equations by applying linear regression analysis. As observed by the statistic analysis, best fitting of curves was found with Freundlich isotherm at the tested range of concentration of the solute (Fig. 2b).

Following form of the Freundlich equation was employed: [START_REF] Karlin | Authigenic magnetite formation in suboxic marine sediments[END_REF] Where q e (µmol g -1 ) is the sorbed concentration, C e (µmol L -1 ) is the equilibrium concentration at the end of the experiment, while K F and n are the Freundlich constants.

Heterogeneity factor (n) can characterize this expression and thus, the heterogeneous systems can be described by Freundlich isotherm. Determination of Freundlich constants is enabled by plotting logC s versus logC e (Table 2). The Freundlich exponents are much smaller than unity for all solids. On the basis of sorption coefficients, the order of NA affinity was M1 > M2 > 2). Solid phase extraction showed a good mass balance, indicating the sole process was NA sorption without any molecular transformation on the surface of magnetite.

n e F e C K q / 1  M3 (Table
The observed sorption behaviour vs. pH can be linked to a blend of pH-dependent NA speciation and the surface charge properties of the iron oxides (Fig. 2c). The adsorption envelope of monoprotic organic acids attached to iron oxide by inner sphere surface complexation usually represented highest adsorption at a pH near the pK a (pKa of NA = 5.95) [START_REF] Tanis | Experimental and modeling studies of sorption of tetracycline onto iron oxides-coated quartz[END_REF][START_REF] Hanna | Sorption of two naphthoic acids to goethite surface under flow through conditions[END_REF][START_REF] Hanna | Sorption of two aromatic acids onto iron oxides: Experimental study and modeling[END_REF]]. An increase in NA sorption onto hydrous oxides was found firstly with an increase in pH, where NA is protonated and particles of Fe-oxide contained positive charge.

Charge repulsion was expected at pH above 7 where both sorbent and sorbate were negatively charged.

The effect of sodium chloride (NaCl) addition at various ionic strengths (ranging from 0.001 to 1 M) was tested at 20 °C and pH 6.5 (data not shown). Increasing the concentration of monovalent cation caused a slight decrease in sorption (less than 5% for M1 and about 8% for M2 and M3) which suggested a stronger sorption mechanism of NA onto the surface of iron oxides than non-specific electrostatic interactions. Moreover, according to coagulation theory, cations should enhance particle aggregation which increases with an increase in ionic strength or NaCl concentration. As the ionic strength effect is less significant, the particle aggregation state must be of less importance. However, sorption of NA was highly decreased with an increase in phosphate concentration and completely inhibited at 1 mM (data not shown).

Indeed, the presence of a strong binding ligand such as phosphate hinders the surface sites of the sorbent and thus no NA sorption will occur.

FTIR data interpretation:

The FTIR spectra of NA sorbed on magnetites were plotted only in the wavenumbers ranging from 1300 to 1800 cm -1 (Fig. 3). The vibration band assignments of the IR spectrum of the pure NA made by Gunasekaran and co-workers [START_REF] Gunasekaran | Vibrational spectra and normal coordinate analysis of nalidixic acid[END_REF] were used here to interpret the IR spectra. Firstly, the carboxylic acid C-O stretching band (around 1327 cm -1 ) was shifted to 1375 cm -1 when NA is sorbed on M1 (Fig. 3). Strong bands at 1712 cm -1 and 1675 cm -1 are assigned for C=O carbonyl stretching and C=O carboxylic acid stretching, respectively [START_REF] Gunasekaran | Vibrational spectra and normal coordinate analysis of nalidixic acid[END_REF]. These two vibration bands shifted to 1745 cm -1 and 1711 cm -1 after NA adsorption on M1 (Fig. 3). This shift could be linked to a coordination bond formed between the C=O group and the Fe site or to the hydrogen bonding between the carbonyl and hydroxyl groups on the surface of magnetite. Slight shift to high wavenumbers was also observed after adsorption onto magnetite (Fig. 3) for the bands attributed to C = C (1560, 1617, 1456 and 1544 cm -1 ) and C = N (1385, 1473, 1409 and 1519 cm -1 ) stretching vibrations [START_REF] Gunasekaran | Vibrational spectra and normal coordinate analysis of nalidixic acid[END_REF]. All these observations confirm the presence of strong chemical interactions involved in the adsorption of NA on magnetite. Wu and co-workers [START_REF] Wu | Adsorption of the quinolone antibiotic nalidixic acid onto montmorillonite and kaolinite[END_REF] have analyzed the NA sorption onto clays by FTIR and reported that NA adsorption took place via a coordination bond formed between the keto oxygen and/or the C-N group in the pyridine ring and the montmorillonite surface, while electrostatic and hydrophobic interactions are rather dominant during sorption of NA onto kaolinite.

The spectrum of NA sorbed on M2 in the 1300-1800 cm -1 was close to that of the M1 except that the absorption bands are less intense, suggesting the occurrence of similar interactions on both nanosized magnetites. However, the spectrum of NA sorbed on the microsized magnetite (M3) exhibits broader and lesser intense bands with a slight shift for the main bands. Lower sorption on M3 makes it difficult to describe accurately the NA surface speciation.

Column study

Breakthrough curves and sorption capacity in column. Firstly, column breakthrough curves (BTC) of bromide were established for all column tests and found nearly identical. High recovery rate of injected bromide (97%) indicates mass conservation and an inert nature of the interactions between iron oxides and bromide. Flow is considered homogeneous as the mobile fraction is around 90%. Macroscopic dispersivity of the medium was calculated by using the ratio between the dispersion coefficient (D m ) and the pore velocity. Molecular diffusion was considered negligible with respect to the dynamic dispersion. Indeed, effective molecular diffusion coefficient is around 10 -6 cm 2 ∕s which generally decreased with an increase in aqueous solubility. The calculated D m lies at 0.002 cm 2 /min, while the dispersivity  was around 200 µm, close to the grain size particle. The Péclet number (Pe = vL/D) was higher than 300 in the column, indicating the predominance of a convective regime in all column tests.

The BTC of NA from the three packed columns at a flow rate of 0.2 ml.min -1 are presented in Figure 4. The breakthrough point, curve steepness and the complete breakthrough strongly depend on the type of magnetite employed. For instance, the breakthrough point for NA in M1 column starts at ~35 PV and is completed at ~60 PV, while for M2 the complete breakthrough occurred at around 30 PV (Fig. 4a; C 0 = 50 µM). The pH of inflow solution of NA was around 6.0. But an increase in pH of outflow solution H was observed from about 5.0 to about 5.5 and slowly followed NA breakthrough throughout experiment (not shown).

Maximum coincidence of the pH was observed with the breakthrough slope of NA. Influent value of 6 ± 0.1 was only regained when steady state was attained by solute sorption and complete breakthrough (data not shown).

The adsorption front in the BTC of M1 is diffuse, thereby underscoring the effect of kinetic, nonlinear sorption and/or physical dispersion. Shape of the isotherm might be reflected by this diffuse adsorption front when chemical equilibrium was achieved on the time scale of the column tests. For instance, a concave isotherm involves diffuse adsorption front in the sand packed column [START_REF] Bürglsser | Determination of nonlinear adsorption isotherms from column experiments: An alternative to batch studies[END_REF]. Present study provides a proper description of the sorption isotherms with the Freundlich model (Table 2, where the Freundlich exponents are much smaller than unity).

Sorbed amount in column was determined by calculating the total area above the breakthrough curve, which represents the amount of solute sorbed by the solid mass from the break point to complete breakthrough. The sorbed amounts determined at complete breakthrough for all the columns are reported in Table 3. The BTC were determined at a lower flow rate to ensure a high residence time and to reach local equilibrium in the column.

Comparison between the sorbed amounts for both methods represents a discrepancy between batch and column data. This may come in part from the leaching of Fe reactive species from the column or the loss of sorbent particles. To determine if the reactive phases were flushed out of the column, Fe content was analyzed in the effluent of columns blank test injected with background electrolyte (without NA). In case of M3 (microsized magnetite), total Fe was found very low corresponding to less than 2 mg of magnetite in the effluent (< 1%). For M1 or M2, the total amounts of mobilized Fe would correspond to about 10 % of magnetite present in the column. Nanoparticles can be flushed out of the column, thus reduce slightly the sorption capacity of the column system. However, further measurements showed that injection of NA can enhance particle mobilization, as more Fe was observed in the effluent of columns fed with NA solution. Therefore, mobilization of magnetite particles upon both water saturation and NA solution injection involved a slight fall in sorption observed in the flow system.

To confirm this behavior, BTCs for three M columns were evaluated according to the previous tests but by using fluoride as a reactive tracer. Fluoride was chosen as a model compound because of large amount of literature describing the interactions of fluoride with iron oxides [START_REF] Sigg | The interaction of anions and weak acids with the hydrous goethite (α-FeOOH) surface[END_REF]. The breakthrough finds represented a slight disparity between batch and column data. This observation pointed out the direct relation of such behavior with the loss of nanoparticles from the column, and not to the specific interactions of NA with oxide.

The retardation factor is important to characterize the transport of a solute in the convectiondispersion model. The retardation factor is concentration-independent in case of linear sorption. For nonlinear sorption, the retardation factor is concentration-dependent. Batch experiments can be used to determine retardation factors. The distribution coefficient K d and the retardation factor R can be linked as:

d K R     1 ( 8
)
Where ρ is the bulk density (g/cm 3 ), θ the volumetric water content, and K d the sorption distribution coefficient (cm 3 /g).

For the Freundlich isotherm, the partition coefficient can be given by:

d n F e K C n K C q   1 / 1 1   (9)
and the retardation factor is given as [START_REF] Zheng | Applied Contaminant Transport Modeling[END_REF][START_REF] Sharma | Geoenvironmental engineering: site remediation, waste containment, and emerging waste management technologies[END_REF]:

1 / 1 1 1    n F C n K R   (10)
The retardation factors estimated from eq.10 are reported in Table 4. The retardation factors for NA were also determined from moment analysis of the experimental BTC by assuming that sorption equilibrium was attained in the column system, and are presented in Table 4. As for the sorbed amounts, there is a disparity between the R values estimated from batch and column data.

Modeling of breakthrough capacities in column.

Semi-empirical models such as the Thomas, Yan and Yoon-Nelson models are used to estimate the sorption extent under flow through conditions and to assess the breakthrough capacity from the break through curves.

The Thomas model is usually employed to estimate the extent and rate constant of sorption [START_REF] Srivastava | Use of NADH fluorescence measurement for on-line biomass estimation and characterization of metabolic status in bioreactor cultivation of plant cells for azadirachtin (a biopesticide) production[END_REF][START_REF] Martínez-Lladó | Sorption and mobility of Sb(V) in calcareous soils of Catalonia (NE Spain): Batch and column experiments[END_REF]. This model assumes that the external as well as the internal diffusions do not act as limiting step, as it is demonstrated above in our tested systems. However, Thomas model assumes the Langmuir isotherm for equilibrium and a second order reaction for kinetics [START_REF] Srivastava | Use of NADH fluorescence measurement for on-line biomass estimation and characterization of metabolic status in bioreactor cultivation of plant cells for azadirachtin (a biopesticide) production[END_REF],

while Freundlich isotherm provides a good description of our sorption isotherms.

Expression of model in linear form gives: [START_REF] Ruby | Synthesis and transformation of iron-based layered double hydroxides[END_REF] where k T is the Thomas rate constant (ml min -1 µmol -1 ), q e is the equilibrium sorbed per g of the sorbent (µmol g -1 ), Q is the volumetric flow rate (ml min -1 ), V is the effluent volume (ml) and m is the sorbent mass in column (g). A linear plot of ln[(C 0 /C) -1] against V/Q (or t) allows to determine k T and q e values from the intercept and the slope of the plot, respectively.

Poor r 2 values were achieved by the Thomas model, suggesting an inaccurate description of all breakthrough data by the said model (Table 3). In spite of the poor r 2 values, sorbed amount predicted by the Thomas model is in relatively good agreement with sorption capacities calculated by integrating the total area above the BTC (Table 3). The values of K T and q e were affected by influent concentration: q e increased while k T decreased with increasing influent concentration of NA.

The Yan model is an empirical model that can overcome the Thomas model deficiency in predicting the concentration at t= 0 [START_REF] Yan | A new model for heavy metal removal in a biosorption column[END_REF]. The Yan model is supposed to provide more accurate description of different parts of the BTC [START_REF] Yan | Heavy metal removal in a biosorption column by immobilized M. rouxii biomass[END_REF]. Experimental data can be fitted through the following equation: [START_REF] Usman | FeII induced mineralogical transformations of ferric oxyhydroxides into magnetite of variable stoichiometry and morphology[END_REF] Where a and d are the constants of the Yan model, with d = q y m/C 0 and a = k y C 0 /Q; k Y = kinetic rate constant for the Yan model (ml min -1 µmol -1 ), and q y = maximum adsorption capacity (µmol g -1 ) of the adsorbent estimated by the Yan model.

Yan model yielded satisfactory values of r 2 suggesting that it can accurately describe all breakthrough data (Table 3). A good agreement was observed between the predicted sorbed amount and the sorption capacity (Table 3). As for the Thomas model, the values of Yan model parameters depend on the influent concentration: k Y decreased with increasing influent concentration of NA.

The Yoon-Nelson model was also employed as a descriptive model [START_REF] Yoon | Application of gas adsorption kinetics I. A theoretical model for respirator cartridge service life[END_REF]. This model in linearized form for a single component system is described as:

(13) Q V C k Q m q k C C T e T 0 0 1 ln          YN YN k t k C C C             0 ln a d V C C          1 1 1 0
where k YN is the Yoon-Nelson rate constant (min -1 ), and τ is the time required for 50% adsorbate breakthrough. The Yoon-Nelson model gives the poorest r 2 values, and therefore it is not considered in the calculation of BTC.

BTCs were only calculated with Thomas and Yann models using the fitting parameters, and are presented as solid lines in Figures 4 and5. Both Yan and Thomas model fit relatively well the breakthrough curves of NA adsorption, but the best fitting was obtained with the Yan model (Fig. 5). Calculated and experimental BTC were in good agreement with each other for all magnetites. Thomas model failed particularly to predict an accurate concentration at lower and higher time points of the BTC, especially for M2 (Fig. 4).

Conclusions

Particle size and surface properties of tested magnetite strongly affected the kinetics and extent of NA sorption. The kinetic sorption experiments showed that apparent rate constant normalized to solid mass, is faster for the nanosized magnetite while an opposite trend was observed for the surface area-normalized rate constants. The aggregation state of the particles did not affect the sorption extent or rate. FTIR data suggested that similar surface interactions occurred on both microsized and nanosized magnetites. Experimental and modeling data suggested that transport of NA under flow through conditions was linked to the instantaneous sorption and no significant impact of chemical kinetic limitation was observed. Less than 10% of nanoparticles can be flushed out of the column, thereby resulting in slight decrease in sorption capacity of the column system. Three semi-empirical models Thomas, Yoon-Nelson and Yan models were employed to estimate the amount of NA sorbed in the column. The sorbed amount predicted by Thomas or Yan model was in good agreement with sorption capacities calculated by integrating the total area above the BTC. However, Thomas model failed particularly to predict accurately the concentration at lower and higher time points of the BTC, especially for M2. These findings have strong implications in relation to transport and removal of environmental pollutants in natural and engineered systems.

Tables

Figures captions

Figure 1 :

 1 Figure 1: XRD (a) and TEM (b) of the three used magnetites (M1, M2 and M3).

Figure 2 :

 2 Figure 2: (a) Sorption onto three M vs. time. Solid= 0.5 g/L; [NA] = 200 µM; pH = 6.5 ± 0.1. Lines represent kinetic model fits. (b) Sorption isotherms onto M1, M2 and M3. Solid= 0.5 g/L; pH = 6.5 ± 0.1. (c) Sorption onto three M vs. pH. Solid= 0.5 g/L; [NA]= 50 µM. Conditions: T = 20 ±1 °C, pH = 6.5 ± 0.1, NaCl (10 mM) was used as a supporting electrolyte.

Figure 3 :

 3 Figure 3: FTIR of of NA sorbed on M1, M2 and M3. Solid= 0.5 g/L; [NA]= 200 µM, T = 20±1 °C, pH = 6 ± 0.1, NaCl (10 mM) was used as a supporting electrolyte.

Figure 4 :

 4 Figure 4: Experimental breakthrough curves of Br -and NA; Flow rate = 0.2mL/min. Experimental data (symbols) and calculated breakthrough curves (solid lines) by Thomas model. 0.5 g was the amount of reactive phase in each column test. Inflow solution with (a) C 0 = 50 µM; (b) C 0 = 200 µM; pH= 6 ± 0.1; T= 20 °C, NaCl (10 mM), [Br -] = 10 -2 M.

Figure 5 :

 5 Figure 5: Experimental breakthrough curves of Br -and NA; Flow rate = 0.2mL/min. Experimental data (symbols) and calculated breakthrough curves (solid lines) by Yan model. 0.5 g was the amount of reactive phase in each column test. Inflow solution with (a) C 0 = 50 µM; (b) C 0 = 200 µM; T=20 °C, pH= 6 ± 0.1; NaCl (10 mM), [Br -] = 10 -2 M.

Fig. 1 :

 1 Fig. 1:

2.1. Chemical Reagents

	Nalidixic acid (NA), sodium phosphate (Na 3 PO 4 . 12H 2 O), ferrous chloride tetrahydrate
	(FeCl 2 . 4H 2 O), ferrous sulfate heptahydrate (FeSO 4 •7H 2 O) and ferric chloride hexahydrate
	(FeCl 3 . 6H 2 O) were provided by Sigma Aldrich. Fontainebleau sand (France) was purchased
	from Prolabo (grain size range = 100-250 µm).

Table 1 . Main characteristics of three magnetites

 1

	Magnetite	Mean	SSA GEO	SSA BET	PZC	P s
	samples	particle size	(m 2 g -1 )	(m 2 g -1 )		(mol L -1 )
	M1	30 nm	38	103 ±2	7.9	29.0
	M2	60 nm	19	25 ± 1	7.7	7.1
	M3	1.5 µm	1.8	1.7± 0.1	7.4	0.5

Table 2 . Equilibrium and kinetic parameters obtained when the experimental data was fitted to the Freundlich isotherm and the pseudo-second order model.

 2

		Kinetic parameters		Equilibrium parameters
	Solid	q e (µmol g -1 )	k 2 min -1 ) (g µmol -1	r 2	K F	1/n	r 2
	M1	172.4	1.85E-04	0.9997 2.97E-02 0.550	0.9954
	M2	74.6	1.26E-03	0.9998 9.80E-02 0.766	0.9945
	M3	16.0	2.22E-02	0.9997 2.42E-03 0.589	0.9889

Table 3 : Experimental sorbed amount in column and Thomas model parameters for NA sorption at tow feed concentrations: 50 µM and 200 µM.

 3

	solid Sorption amount in				Thomas model
		column (µmol g -1 )
					q e			k th	r 2
				(µmol g -1 )	(ml µmol -1 min -1 )
		50 µM	200 µM 50 µM 200 µM 50 µM 200 µM 50 µM 200 µM
	M1	51.2	132.8	50.01	140.4	0.101	0.036	0.96	0.96
	M2	26.7	55.6	27.7	58.5	0.138	0.041	0.92	0.91
	M3	5.5	14.1	5.9	13.9	0.63	0.140	0.84	0.86
	Yan model parameters
	solid				Yan model
			k Y		q y			r 2
		(ml µmol -1 min -1 )		(µmol g -1 )
		50 µM	200 µM	50 µM	200 µM	50 µM	200 µM
	M1	42.4E-03	10.6E-03	48.3	137.2	0.95	0.95
	M2	34.8E-03	9.4E-03	27.0	60.0	0.97	0.95
	M3	30.0E-03	8.1E-03	5.7	15.2	0.86	0.88
	Yoon-Nelson model parameters
	solid			Yoon-Nelson model
		τ		k YN			r 2
		(min)		(min -1 )
		50 µM 200 µM	50 µM 200 µM	50 µM 200 µM
	M1	2390	1684	0.0031 0.0044		0.88	0.88
	M2	1273	756	0.0041 0.0084		0.92	0.90
	M3	286	186	0.017	0.030		0.80	0.84

Table 4 : Retardation factors derived from batch and column tests

 4

	Sorbent		Batch		Column
		50 µM	200 µM	50 µM	200 µM
	M1	60.9	33.1	41.0	29.0
	M2	33.4	24.4	22.5	12.0
	M3	4.6	3.1	4.9	3.3

Acknowledgements

The authors gratefully acknowledge the financial support provided by CNRS (Centre Nationale de la Recherche Scientifique) of France and Higher Education Commission (HEC) of Pakistan.