Hajer Maraoui
email: hajer.maraoui@gmail.com

Kais Haddar
email: kais.haddar@yahoo.fr

Laurent Romary
email: laurent.romary@inria.fr

Encoding prototype of Al-Hadith Al-Shareef in TEI

Keywords: Hadith text, TEI model, standardization, prototype. 1

The standardization of Al-Hadith Al-Shareef can guarantee the interoperability and interchangeability with other textual sources and takes the processing of Al-Hadith corpus to a higher level. Still, research works on Hadith corpora had not previously considered the standardization as real objective, especially for some standards such as TEI (Text Encoding Initiative). In this context, we aim at the standardization of Al-Hadith Al-Shareef on the basis of the TEI guidelines. To achieve this objective, we elaborated a TEI model that we customized for Hadith structure. Then we developed a prototype allowing the encoding of Hadith text. This prototype analyses Hadith texts and automatically generates a standardized version of the Hadith in TEI format. The evaluation of the TEI model and the prototype is based on Hadith corpus collected from Sahih Bukhari. The obtained results were encouraging despite some flaws related to exceptional cases of Hadith structure.

Introduction

The processing of Al-Hadith Al-Shareef has always been a center of academic interest. On the one hand, this interest is due to the importance of Al-Hadith Al-Shareef in Islamic law. It is the second fundamental source, after the Quran, of Islamic legislation. On the other hand, linguistic researches on Arabic language define Al-Hadith corpus as one of references for classical Arabic from the pre-Islamic era. Many studies carried out on the Al-Hadith corpus especially in linguistic analyses and information retrieval. However, the representation of such corpora poses serious structuring and text unification problems, which require their standardization (or normalization). This could lead to a new presentation of the Text based upon a descriptive and detailed annotation for each of its parts. A normalized corpus allows also the compatibility and the interchangeability between NLP applications. Indeed, the normalization of Al-Hadith Al-Shareef can bring the automatic processing of such corpus to another level.

However, normalizing Al-Hadith corpus is a complex task. In fact, it requires a specific model customized for standardizing the Hadith text. This task requires the selection of the standardization model that harmonizes with Arabic language in general and Al-Hadith structure specifically. Moreover, to realize a normalized Hadith corpus, an automatic encoding process can facilitate this task.

Our main objective is the normalization of Al-Hadith Al-Shareef. To realize this, we start with a deep study on Hadith text structure. Furthermore, to reach the normalization of Al-Hadith Al-Shareef, we apply the Text Encoding Initiative (TEI) (http://www.tei-c.org/) guidelines. We elaborate a TEI customized model for encoding Hadith text. Also, to create a normalized Hadith corpus, we make a prototype to create automatically an encoded version of Al-Hadith text with TEI structure.

In the present paper, we begin with a state of the art on Al-Hadith Al-Shareef. Second, we continue with an overview on TEI guidelines. Third, we present our model for encoding Hadith text. Then, we present our prototype for constructing a normalization of Hadith texts with TEI structure. This section is followed by an evaluation step. We cloture our paper with a conclusion and some perspectives.

State of the Art on Al-Hadith Al-Shareef

Hadiths (or prophetic traditions) are narrations on the life and deeds of Prophet Muhammad (peace and blessing upon him), which report what he said or did, or of his implicit approval of something said or done and by itself define what is considered good, by providing details to regulate all aspects of life in this world and to prepare people for the beyond, clarifying the Qur'anic shades. The traditional Muslim schools of jurisprudence regarding Hadith constitute an important tool for understanding Qur'an and in all matters related to jurisprudence [1][2]. The Hadith consists of two parts: the actual narration, which called Matn ;)المتن( and the chain of narrators who has transmitted the narration, known as Isnad .)إسناد( The Isnad consists of a short or long chronological list of the narrators, each mentioning the one from whom he heard the Hadith all the way to the prime narrator of the Matn followed by the Matn itself [START_REF] Dalloul | Partial Fulfillment of the Requirements for the Degree of Master in Information Technology[END_REF].

Research in the Isnad is very important in the science of Hadith. Islamic scholars have agreed that Isnad is required to prove the accuracy and the soundness of the Hadith which means that any flaw in the chain of transmitters lead to the negation of the Hadith. In order to know whether the Hadith is authentic or not, the Hadith scholars follow clear steps in the judgment on the Hadith Isnad that considered as traditional methods. Sahih Bukhary and Sahih Muslim are the recognized collection of authentic assortment of the Sunna [1] [3-5].

Nowadays, software tools help judge the Hadith Isnad like electronic Hadith encyclopedias and some websites. Additionally, information retrieval and search engines that related to semantic web can used to serve in deciding the degree of the Hadith Isnad. Scholars such as Al-Albani have agreed and encouraged using computers and programs in serving religion and Hadith [START_REF] Dalloul | Partial Fulfillment of the Requirements for the Degree of Master in Information Technology[END_REF].

There are many projects handled with Hadith corpus. Indeed, these projects focused on several branches of researches such as Hadith ontology, linguistic analyzing, Hadith segmentation, authorship attribution, classification and the mining of information.

In [START_REF] Boella | The SALAH Project: Segmentation and Linguistic Analysis of hadῑṯ Arabic Texts[END_REF], the researchers proposed a model for the unsupervised segmentation and the linguistic analysis of the Arabic texts of Hadith. This model is named SALAH. The model automatically segments each text unit in a transmitter chain Isnad and text content Matn. A tailored, augmented version of the AraMorph morphological analyzer (RAM) analyzes and annotates lexically and morphologically the text content. A graph with relations among transmitters and a lemmatized text corpus, both in XML format, are the final output of the system.

In [START_REF] Dalloul | Partial Fulfillment of the Requirements for the Degree of Master in Information Technology[END_REF], the autor constructed an ontology-based Isnad Judgment System (IJS) that automatically generates a suggested judgment of Hadith Isnad. It based on the rules that Hadith scholars follow to produce a suggested judgment. A prototype of the approach implemented to provide a proof of concept for the requirements and to verify its accuracy.

Authors of paper [START_REF] Baraka | Building Hadith Ontology to Support the Authenticity of Isnad[END_REF] built a domain specific ontology (Hadith Isnad Ontology) to support the process of authenticating Isnad. They evaluate the ontology through Hadith example and DL-Queries.

Author of paper [START_REF] Alkhatib | Classification of Al-Hadith Al-Shareef using data mining algorithm[END_REF] compared the effectiveness of four different automatic learning algorithms for classifying Hadith corpus into 8 selective books depending on Sahih Bukhary. The automatic learning algorithms are Rocchio algorithm, K-NN algorithm (K-Nearest Neighbor), Naïve Bayes algorithm and SVM algorithm (Support Vector Machines).

In [START_REF] Azmi | iTree -Automating the Construction of the Narration Tree of Hadith[END_REF], the authors reported on a system that automatically generates the transmission chains of a Hadith and graphically display it. They involve parsing and annotating the Hadith text and identifying the narrators' names. They use shallow parsing along with a domain specific grammar to parse the Hadith content.

In [START_REF] Sayoud | Author discrimination between the Holy Quran and Prophet's statements[END_REF], the author experimented author discrimination techniques between the Qur'an and the Hadith. The Qur'an is taken in its entirety, whereas for the Prophet's statements, the researcher chose only the certified texts of Sahih Bukhari. Three series of experiments are done and commented on. The author's investigation sheds light on an old enigma, which has not been solved for 14 centuries: in fact, all the results of this investigation have shown that the two books should have two different authors.

In [START_REF] Saloot | Hadith data mining and classification: a comparative analysis[END_REF], the researchers reimplemented and evaluated the methods of artificial intelligence using a single dataset. The result of the evaluation on the classification method reveals that neural networks classify the Hadith with 94% accuracy. The Hadith mining method that combines vector space model, Cosine similarity, and enriched queries obtains the best accuracy result.

The Text Encoding Initiative

The Text Encoding Initiative (TEI) is an international project aiming at the development of a set of standards for the preparation and the exchange of electronic texts. The TEI was founded in November 1987 by a group of international text database leaders. TEI was created officially in 1988 under the aegis of the ACH 1 , the ACL 2 and the ALLC 3 [START_REF] Dalloul | Partial Fulfillment of the Requirements for the Degree of Master in Information Technology[END_REF].

The publication of the works of the various committees' results was in the form of "Guidelines" which have been developed and are maintained by the Text Encoding Initiative Consortium [START_REF] Burnard | TEI P5: Guidelines for Electronic Text Encoding and Interchange, Text Encoding Initiative Consortium[END_REF]. The TEI guidelines recommend suitable ways to represent the features of textual resources using a set of XML elements in order to elicit the text structure and simplify its digital processing. Indeed, these guidelines present conventions of usable coding in several domains and can be applied to texts in any natural language, of any date, in any literary genre or text type [START_REF] Burnard | TEI P5: Guidelines for Electronic Text Encoding and Interchange, Text Encoding Initiative Consortium[END_REF]. Moreover, they can be applied as well to create new information that to exchange existing information.

TEI annotation is based on a "patrimonial" transcription of the text, interested in giving as much information as possible while allowing automatic processing for language searches, historical data, different versions of the document and variations level of accuracy that can be adapted to the desired searches [START_REF] Dufournau | Manuel d'encodage XML-TEI Renaissance et temps modernes Imprimés-manuscrits[END_REF]. TEI offers the possibility of multilingual uses of the structural description. The universality of the elements allows the compatibility of the analyzes, and the digitized sources within such frameworks as the BVH 4 and belong to all encyclopedic domains, in several ancient and modern languages.

The rules and recommendations made in these guidelines are expressed in terms of the extensible Markup Language (XML) so a TEI document has to comply with XML coding rules. One of the main advantages of the XML language is that it is possible to solve by encoding the very large typographic and textual variation of the documents: this flexibility should not, however, be a hindrance to the acquisition and encoding of textual corpora.

The fundamental structure of a TEI document describes the textual part of the text. In what follows, we give overviews onto the structure and the TEI representation of documents. The basic structure of a document encoded with TEI is represented as follow:

<TEI xmlns="http://www.tei-c.org/ns/1.0"> <teiHeader> <!--Header properties; meta-data --> </teiHeader> <text> 1 Association for Computers and the Humanities 2 Association for Computational Linguistics 3 Association for Literary and Linguistic Computing

<front> <!--front information --> </front> <body> <!--main body --> </body> <back> <!--back information --> </back> </text> </TEI>
Any textual document encoded with TEI includes a document header, with the <teiHeader> element, and a text part within the <text> element. TEI header contains all the information analogous to that provided by the title page of a printed document. It has four parts: a bibliographic description of the machine-readable text, a description of the way it has been encoded, a text profile, and a revision history [START_REF] Dufournau | Manuel d'encodage XML-TEI Renaissance et temps modernes Imprimés-manuscrits[END_REF][START_REF] Ide | Une application de la TEI aux industries de la langue: le Corpus Encoding Standard[END_REF][START_REF] Burnard | La TEI Simplifiée : Une introduction au codage des textes électroniques en vue de leur échange[END_REF].

A TEI document can contain five textual elements: <text>, <front>, <group>, <body> and <back>. Only <text> and <body> are the obligatory elements. The use of the <front>, <group> and <back> is optional. The <front> element is defined to cluster together the pieces located before the beginning of the text itself. The <back> element is used in case the document contains an annex in the back of the text. The <group> element is specified to include several texts in collections. The <body> is included in the text and it contains the core text of the document [START_REF] Dufournau | Manuel d'encodage XML-TEI Renaissance et temps modernes Imprimés-manuscrits[END_REF].

Personalization is a central aspect of TEI using. There are three methods of customization in TEI: TEI Lite, web application Roma and TEI ODD. TEI Lite was originally designed as a demonstration of the customization mechanism. The Roma web application was introduced to select TEI modules that manipulate the elements. As for TEI ODD language, it essentially allows the manual specification of the TEI models, allowing the modification or addition of new elements [START_REF] Burnard | TEI P5: Guidelines for Electronic Text Encoding and Interchange, Text Encoding Initiative Consortium[END_REF].

Encoding quotation with TEI

Quotation marks are conventionally used to indicate certain elements appearing in a text, the most frequent case is for the quotation. However, the marking of the underlying logical element (for example, a quotation or a piece of direct speech) in the text is recommended, rather than just recording quotation marks in the text [START_REF] Burnard | TEI P5: Guidelines for Electronic Text Encoding and Interchange, Text Encoding Initiative Consortium[END_REF][START_REF] Dufournau | Manuel d'encodage XML-TEI Renaissance et temps modernes Imprimés-manuscrits[END_REF][START_REF] Ide | Une application de la TEI aux industries de la langue: le Corpus Encoding Standard[END_REF]. The following TEI elements are specified for the encoding of quotation and narration which can be adaptable with the structure of Al-hadith Matn:

• <q> (or quoted) contains material which is distinguished from the surrounding text using quotation marks or a similar method. It contains a citation or an apparent citation -the representation of a speech or thought, marked out to indicate that it is a quotation. Among the possible attributes there are:

─ The @type attribute: it can be used to indicate whether the quoted passage is pronounced or simply thought, or to characterize it more finely: possible values are: spoken (for the representation of direct speech, usually marked by quotation marks) and thought (for the representation of thoughts, for example, internal monologue). ─ The @who attribute: it identifies the speaker in the case of a direct speech passage.

• <said> (speech or thought) indicates passages thought or spoken aloud, whether explicitly indicated in the source or not, whether directly or indirectly reported, whether by real people or fictional characters. • <quote> (quotation) contains a phrase or passage attributed by the narrator or author to some agency external to the text.

The <q> element may be used if no further distinction beyond this is judged necessary. If it is felt necessary to distinguish such passages further, for example to indicate whether they are regarded as speech, writing, or thought, either the type attribute or one of the more specialized elements discussed in this section may be used. For example, the element <quote> may be used for written passages cited from other works, or the element said for words or phrases represented as being spoken or thought by people or characters within the current work. If the distinction among these various reasons why a passage is offset from surrounding text cannot be made reliably, or is not of interest, then any representation of speech, thought, or writing may simply be marked using the q element. Quotation may be indicated in a printed source by changes in type face, by special punctuation marks (single or double or angled quotes, dashes, etc.) and by layout (indented paragraphs, etc.), or it may not be explicitly represented at all.

Encoding person name with TEI

The TEI guidelines present several models for encoding a set of types of named entities. One of these models aims to annotate person names. This can cover the annotation of all the information related with the person name (such as first name, family name, additional name, etc.). To conduct nominal record linkage or even to create an alphabetically sorted list of personal names, it is important to distinguish between a family name, a forename and an honorary title. Similarly, when confronted with a string such as اب' ّ الخط ابن عمر حفص أبي المؤمنين 'أمير ('Prince of the Believers Abu Hafs Umar Ibn Al-Khattab'), the analyst will often wish to distinguish amongst the various constituent elements present, since they provide additional information about the status, the occupation, or the residence of the person to whom the name belongs. The following TEI elements are provided for encoding person name and related purposes.

• <persName> (personal name) contains a proper noun or proper-noun phrase referring to a person, possibly including one or more of the person's forenames, surnames, honorifics, added names, etc. • <surname> contains a family name, as opposed to a given, baptismal, or nick name.

• <forename> contains a forename, given or baptismal name.

• <roleName> contains a name component which indicates that the referent has a particular role or position in society, such as an official title or rank. • <addName> (additional name) contains an additional name component, such as a nickname, epithet, or alias, or any other descriptive phrase used within a personal name.

• <nameLink> (name link) contains a connecting phrase or link used within a name but not regarded as part of it, such as "de" or ."بن" • <genName> (generational name component) contains a name component used to distinguish otherwise similar names on the basis of the relative ages or generations of the persons named.

We were inspired by TEI models for encoding quotation and person information to build a model for Hadith text encoding. The following section illustrates this model who was improved to encode Matn and Isnad of Hadith text.

Proposed model for Hadith encoding with TEI

In this section, we present our proposed encoding model shaped for Hadith text and inspired from the TEI guidelines. To realize the standardization of Hadith corpus with TEI, we start by the selection of the necessary data categories that harmonized with Hadith text specification. The structure of the Hadith text characterized with the imbrication of the different part of the text: Hadith include Isnad and Matn, and each one of them include other parts. Also, TEI allows the imbrication and the restructuring of several models and elements. We start with the concept of the similarity between the structure of Hadith text is similar to the basic structure of quotations and named entities: considering the Matn text of the Hadith as a quotation and the Isnad as an enchained list of person names. To achieve our initial TEI model for Hadith encoding, we select the adaptable TEI elements for Isnad and Matn from TEI model for encoding quotations and named entities [START_REF] Maraoui | Modeling of Al-Hadith Al-Shareef with TEI, ICEMIS Conference[END_REF].

Starting with the Isnad encoding, we consider that the structure of TEI model for encoding the person name can be developed to create a TEI model conforming with the structure of an Arabic person name. Moreover, we based on the integration and imbrication of TEI elements to represent the chain of Al-Hadith transmitters. Returning to the TEI coding of complex structures in general, person names are presented at least by a single <persName> element. The <persName> element is the one that includes all the person name information. Thus, we use this element for transmitter name annotation.

The structure of the Matn is quite similar to the structure of quotations. In fact, many suggestions were proposed by TEI to encode quotations or narration of the author or transmitted quote mentioned inside the document. We used a TEI model to encode Matn text. Fig. 1 illustrates the basic elements model that we customized to adapt Al-Hadith text structure. The development of a specific TEI model for Al-Hadith texts aims to formulate a TEI structure for the encoding of Al Hadith texts. To this first objective, we select the necessary data categories and the adaptable TEI elements from TEI model for encoding quotations and named entities. Our second objective was the creation of a prototype to generate a normalized Hadith text encoded with TEI model. We present this prototype in the next section.

Elaborated prototype for the automatization of Hadith encoding in TEI

To implement the creation of the encoded Hadith corpus with our TEI model, we proposed a prototype for encoding Hadith text. This prototype is developed to generate automatically the encoded Hadith texts with TEI format. For the implementation, we used some tools and programs. First, we designed our system with UML. Then, we used Oxygen XML Editor to adapt a TEI structure for the encoded of Hadith text. After that, we developed the prototype using JAVA language and the API JDOM Library.

The creation of a normalized Hadith with our prototype can be divided into two steps. First, as an input file, the system requests the user to choose an external Hadith file path with .txt extension which contains a Hadith text. Then, the prototype reads the Hadith text and separate the Isnad from the Matn.

For the Isnad, the system identifies the narrators from the chains of transmitters in the Isnad and encodes each narrator name in a <persName> element. To keep the sequence of the transmitters in order, the system assigns for each <persName> element an "xml:id" attribute which contains as value the order of the narrator in the chains of transmitters. Furthermore, according to Hadith text, the narrator name can contain more than one forename. To organize them in order, the system attribute for each forename a "sort" attribute to sort them by number. This step allows the generation of the encoded chains of transmitters.

For the Matn of the chosen Hadith, the prototype identifies his structure and encloses it in a <said> element. To identify the prime narrator who is the first transmitter of the Hadith, the <said> element get a "who" attribute which contains the reference of the prime narrator as value. In Hadith text, the Matn is characterized by different structures, it could be narrative text with no quotations, or sort of conversations which can contain direct discourses or quotations. It can also contain other person names that need to be identified in the encoding phase. The prototype allows the identification of all these data information. The encoding of each part of the Matn goes line by line: the system identifies the structure of each part and encodes it in a corresponding element, for example, a narrative text identified as a narration an encoded in <p> (paragraph) element or a quotation encoded in <quote> element.

After that, the prototype generates the complete TEI encoded file and save it as an output of the system. The following XML code present an output file from our prototype covering the TEI encoding of the Hadith number 46 from the chapter of Belief from Sahih Al-Bukhari book.

<?xml version="1.0" encoding="UTF-8"?> <TEI xmlns="http://www.tei-c.org/ns/

Evaluation and discussion

To evaluate our prototype, we collected the first 1000 Arabic Hadith text from 14 chapters from Sahih Bukhari book. Consequently, the prototype generates respectively 1000 TEI files representing each Hadith encoded with TEI format. Table 1 illustrates the obtained results. According to the value of precision, we conclude that the value of precision is worth 0.86. Also, the recall value is 0.85. These values provide an F-measure equal to 0.85. Consequently, we conclude that the obtained results are encouraging. Besides, we can say that this prototype is flexible and easy to maintain because it is based on an object-oriented programming language. However, we handled some problems. Some of them are related with the particular Hadith forms which need to integrate more specificity and to develop our TEI model to cover the encoding of the particular and the complex forms of Hadith text.

Conclusion and perspectives

The normalization of Al-Hadith Al-Shareef can take the automatic processing of such corpus to another level. In this work, to attain our main objective, we based on TEI guidelines to elaborate a TEI module customized for Hadith structure. To achieve that, first, we started with a deep study of Hadith text structure. Second, we identified the data categories from the TEI standard register which harmonized with the language specification. After that, we elaborated a prototype for the automatic processing of the encoding of Hadith text with our TEI model. Then, we tested our prototype with a 1000 Hadith text from 14 chapters from Sahih Bukhari book. The elaborated

Hadith corpus Precision

Recall F-score 1000 Hadith 0,86 0,85 0,85 prototype allowed us to generate normalized Hadith texts. As mentioned, the obtained values of measures show that the results obtained from our prototype are encouraging. These results can be used in others levels of analyses.

As perspectives, we want improve our TEI modeling of Al-Hadith Al-Shareef by incorporating other criteria and specifications for deeper encoding of the fundamental fragments of the Hadith. Also, we need to integrate more TEI elements in the Hadith model to reach a deep description for the exceptional part in Hadith structure. Besides that, we want to improve our prototype to generalize our method to cover complex Hadith structures.

Fig. 1 .

 1 Fig. 1. Extraction from the basic TEI encoding model for Hadith text

  أ الرَّ ِر ائ َ ث ، د َجْ ن ِ ْل ه َ أ نْ مِ م ّ وسل عليه هللا ى ّ صل ِ ّللاَّ ِ Our prototype allows as to generate encoded Hadith text with TEI format. To create encoded Hadith corpus, we made an evaluation phase to test the consistency of our prototype and the adaptability and the flexibility of the TEI model for Hadith text. The evaluation phase is presented in the following section.

		<!--encoding of Isnad--> <p> م: ّ وسل عليه هللا ى ّ صل ِ ّللاَّ ول س َ ر َ َال /<قp>
		<p>َا ن َ َّث د َ /<حp> <quote>.» َانَ ض َ م َ ر َام ي ِ ص َ /<«وquote>
		<persName xml:id="p5"> ِيل اع َ ْم س ِ /<إpersName> <p> َ َال /<قp> ></pحدثني><p <persName xml:id="p4"> <forename sort="1"> ِك ال َ /<مforename> <forename sort="2" type="nasab"> <p>: َ ى َ ل َ ع َلْ ه َ َال ق </p> َال ق ؟ ه ْر َي غ َّ <quote>.» َ ع َّ و َ َط ت نْ َ أ َّ ال ِ إ ،َ /<«الquote> <p>: َ َال ق َا ه ْر َي غ َّ ى َ ل َ ع َلْ ه َ َال ق .َ َاة ك الزَّ م ّ وسل عليه هللا ى ّ صل ِ ّللاَّ ول س َ ر ه َ ل َ َر َك ذ َ و َ َال /<قp> <quote>.» َ ع َّ و َ َط ت نْ َ أ َّ ال ِ إ ،َ /<«الquote> <p> هللا ى ّ صل ِ ّللاَّ ول س َ ر َ َال ق . ص ْق ن َ أ َ ال َ و َا َذ ه ى َ ل َ ع يد ِ ز َ أ َ ال ِ ّللاَّ َ و ول َق ي َ و ه َ َر ْب د َ َأ ف َ َال ق و ل ج الرَّ َ م: ّ وسل ></pعليه
		<nameLink> ْن /<بnameLink> <quote>.» َقَ د َ ح َ ل ْ ف َ /<«أquote> ص نْ ِ إ َ <forename> َس ن َ /<أforename> </said>
	</forename> </q>
	</persName> </div>
	<p> ِ ّه م َ ع نْ َ /<عp> </body>
	</text>	<persName xml:id="p3">
	</TEI>	<forename sort="1" type="kunya">
		<nameLink>ى ِ ب َ /<أnameLink>
		<forename> ِ ْل ي َ ه /<سforename>
		</forename>
		<forename sort="2" type="nasab">
		<nameLink> ِ ْن /<بnameLink>
		<forename> ِك ال َ /<مforename>
		</forename>
		</persName>
		<p> نْ َ /<عp>
		<persName xml:id="p2"> ِ يه ِ ب َ /<أpersName> <p> َّه ن َ /<أp>
		<p> َ ع َمِ /<سp>
		<persName xml:id="p1">
		<forename sort="1"> َ ة َ ح ْ ل َ /<طforename>
		<forename sort="2" type="nasab">
		<nameLink> ْنَ /<بnameLink>
		<forename>هللا ِ ْد َي ب /<عforename>
		</forename>
		</persName>
		<p> ول َق /<يp>
	<!--encoding of Matn-->
	<said who="p1">
		<p>
	1.0"> س ْ ول س َ ْم س ي ، ِ َو د ع َ ،ِ ِه ت َوْ ص ُّ ى ِ ر ى َ ل ِ إ ٌ ل ج َ ر َ اء َ ج م: ّ وسل عليه هللا ى ّ صل ِ ّللاَّ ول س َ ر َ َال َق ف ِ َم ْال س ِ اإل ِ ن َ ع ل َ ْأ َس ي َ و ه َا ذ ِ َإ ف َا، َن د ى َّ ت َ ح ول َق ي ا َ م َه ق ْ ف ي َ ال َ و <teiHeader>…</teiHeader> </p> <text> <quote>.» ِ ة َ ْل ي َّ الل َ و ِ م َوْ ي ْ ال في ات َ و َ ل َ ص س َمْ /<«خquote> <body> <div xml:lang="ar"> <q> <p>: َ ى َ ل َ ع َلْ ه َ َال َق /<فp> َال ق َا؟ ه ْر َي غ َّ <quote>.» َ ع َّ و َ َط ت نْ َ أ َّ ال ِ إ ،َ /<«الquote>

Table 1 .

 1 Sammery table for the prototype results.

	Evaluated hadith	Hadith chapter	Total encoded	Encoded correctly	Encoded incorrectly

1000 Hadith 14 chapter of Sahih Bukhari 982 846 136

	273 Hadith chapter of call to prayer of Sahih Bukhari	270	234	36
	066 Hadith chapter of Friday prayer of Sahih Bukhari	066	056	10
	006 Hadith chapter of fear prayer of Sahih Bukhari	006	005	01
	042 Hadith chapter of the two festivals of Sahih Bukhari	041	037	04
	011 Hadith chapter of the Witr prayer of Sahih Bukhari	011	010	01
	007 Hadith chapter of revelation of Sahih Bukhari	007	006	01
	051 Hadith chapter of belief of Sahih Bukhari	051	042	09
	076 Hadith chapter of knowledge of Sahih Bukhari	075	064	11
	113 Hadith chapter of ablutions (wudu') of Sahih Bukhari	112	096	16
	046 Hadith chapter of bathing (ghusl) of Sahih Bukhari	046	039	07
	040 Hadith chapter of menstrual periods of Sahih Bukhari	038	032	06
	015 Hadith chapter of ablution with dust of Sahih Bukhari	014	009	05
	172 Hadith chapter of prayer (salat) of Sahih Bukhari	164	150	14
	082 Hadith chapter of time of the prayer of Sahih Bukhari	081	066	15

Table 1

 1 shows that sometimes for particular Hadith texts, we can obtain erroneous encoding. The total number of obtained encoded Hadith texts is 982. The program succeeded to produce 846 Hadith encoded correctly. However, we found 136 Hadith incorrect or incomplete encoded which require some rectification on our TEI model to obtains more encoding coverage for some particular part in some types of Hadith text. This problem of incorrect or incomplete encoding is related with some exceptions and particular Hadith forms such as irregularity in Matn and Isnad position or combination between two or more chain of transmitters referring a same Matn. Also, the prototype misses the encoding of some Hadith because of their exceptional forms: some Hadiths refer directly to prefix Hadiths and came without Isnad or at least they refer to the Isnad of their prefix Hadiths. Indeed, we estimate the quality of our work manually. Table2illustrates the obtained values of precision, recall and F-score.

Table 2 .

 2 Summary table of the precision, recall and F-score.

The laboratory LI-RFAI (director Jean-Yves Ramel) and the consortium Navidomass (ANR project 2007-2009).


Junsong Peng

Sonia Boscolo
email: s.a.boscolo@aston.ac.uk

Nikita Tarasov

Srikanth Sugavanam

V Dmitry

Christophe Churkin

Finot

Dmitry V Churkin

Christophe Finot

Pulsating Solitons in Mode-Locked Fibre Lasers

Keywords: Dissipative nonlinear systems, mode-locked fibre lasers, extreme soliton pulsations

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Mode-locked fibre lasers, besides being attractive sources of ultra-short optical pulses for many applications, constitute an ideal platform for the fundamental exploration of complex dissipative nonlinear dynamics. Various striking nonlinear phenomena have been experimentally observed in mode-locked fibre lasers, including rogue waves [START_REF] Lecaplain | Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser[END_REF][START_REF] Runge | Raman rogue waves in a partially mode-locked fiber laser[END_REF][START_REF] Liu | Rogue waves in a normal-dispersion fiber laser[END_REF][START_REF] Liu | Dissipative rogue waves induced by long-range chaotic multi-pulse interactions in a fiber laser with a topological insulator-deposited microfiber photonic device[END_REF], soliton molecules [START_REF] Krupa | Real-time observation of dissipative optical soliton molecular motions[END_REF], and soliton explosions [START_REF] Runge | Observation of soliton explosions in a passively modelocked fiber laser[END_REF]. Further, a recent theoretical work using the master-equation approach [START_REF] Chang | Extreme soliton pulsations in dissipative systems[END_REF] has showed that there are regimes of operation where laser oscillators may generate pulsating solitons with extreme ratios of maximal to minimal energies in each period of pulsations. The soliton spectra in these regimes also experience large periodic variations. In this paper, we report on the direct experimental observation of extreme soliton pulsations in a passively mode-locked fibre laser. We capture these kinds of pulsations temporally and spectrally in real time using spatio-temporal intensity dynamics measurements and the dispersive Fourier transformation (DFT) [START_REF] Solli | Amplified wavelength-time transformation for real-time spectroscopy[END_REF][START_REF] Goda | Dispersive Fourier transformation for fast continuous single-shot measurements[END_REF].

The methodology of spatio-temporal dynamics has recently enabled substantial progress in the real-time characterisation of dynamic, non-stationary generation regimes of lasers and soliton interactions in other cavitybased systems [START_REF] Marconi | Vectorial dissipative solitons in vertical-cavity surface-emitting lasers with delays[END_REF][START_REF] Jang | Ultraweak long-range interactions of solitons observed over astronomical distances[END_REF][START_REF] Erkintalo | Bunching of temporal cavity solitons via forward Brillouin scattering[END_REF] owing to the possibility of identifying and tracking individual features embedded in the radiation that are otherwise hidden in the usual one-dimensional intensity measurements [START_REF] Arecchi | Two-dimensional representation of a delayed dynamical system[END_REF]. In this method, the intensity evolution in the laser is traced as it makes round-trip circulations within the laser cavity. Employing wide-bandwidth real-time digital storage oscilloscopes, it is possible to use long-term records of onedimensional intensity versus time information to experimentally arrive at a round-trip resolved, two-dimensional intensity domain representation of the laser dynamics. In the context of fibre lasers, such a technique has helped observe the laminar-turbulent transition in a laser [START_REF] Turitsyna | The laminar-turbulent transition in a fibre laser[END_REF], reveal non-trivial periodicity and long-scale correlations of radiation in partially mode-locked lasers [START_REF] Churkin | Stochasticity, periodicity and localized light structures in partially mode-locked fibre lasers[END_REF], observe soliton instabilities in a passively mode-locked laser [START_REF] Runge | Observation of soliton explosions in a passively modelocked fiber laser[END_REF], and investigate different lasing regimes in quasi-continuous-wave Raman lasers [START_REF] Tarasov | Spatio-temporal generation regimes in quasi-CW Raman fiber lasers[END_REF]. DFT [START_REF] Solli | Amplified wavelength-time transformation for real-time spectroscopy[END_REF][START_REF] Goda | Dispersive Fourier transformation for fast continuous single-shot measurements[END_REF] is a relatively simple but powerful technique to obtain spectral dynamics rather than temporal information on ultrashort time scales: Spectral information is mapped into the time domainusing chromatic dispersion in a long optical fibreand is detected via a high-speed photo-detector and real-time digitisation. This method is increasingly used for spectral measurements of rapid signals across a wide range of diverse application fields and, in recent experiments with mode-locked sources, has been applied to record the build-up of femtosecond mode locking [START_REF] Herink | Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90 MHz frame rate[END_REF] and the internal dynamics of soliton molecules [START_REF] Krupa | Real-time observation of dissipative optical soliton molecular motions[END_REF][START_REF] Herink | Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules[END_REF]. The combination of the real-time spatio-temporal methodology with real-time DFT spectral measurements can provide a time-aligned spatio-and spectro-temporal characterisation of highly dynamic processesa feat that remains possible only in numerical simulations.

EXPERIMENTAL SETUP AND RESULTS

The laser used in our experiment is a mode-locked erbium-doped fibre (EDF) ring laser, sketched in Fig. 1. The laser cavity incorporates a 1.5-m long EDF with normal group-velocity dispersion 65.05 ps 2 /km at 1550 nm, which is pumped through a 980/1550 wavelength-division multiplexer by a 976-nm laser diode. The other fibres are standard single-mode fibres (SMF-28) with a total length of 18.5 m, yielding an anomalous path-averaged cavity dispersion of -15.31 ps 2 /km. The mode-locking mechanism is nonlinear polarisation rotation, facilitated through the inclusion of a combination of two polarisation controllers and an in-fibre polarisation-dependent isolator. A 10:90 fibre coupler extracts 10% of the in-cavity power.

At the laser output, we record the spatio-temporal intensity evolution I(t,T), i.e. the evolution of the instantaneous intensity pattern I(t) over many cavity round-trips T, by a 80-GSa/s real-time oscilloscope (Agilent) together with a 50-GHz fast photo-detector (Finisar). We also measure the ensemble-averaged spectrum using an optical spectrum analyser (OSA) and use the DFT to acquire high-resolution spectral measurements at the shot-to-shot level. The DFT is implemented by temporally stretching the laser output in a normally dispersive fibre of length L ≈ 11 km, providing a total accumulated dispersion of |D|L = 1200 ps/nm. This maps the pulse spectra into the temporal domain, allowing us to measure them in real time. Our DFT configuration allows shot-to-shot measurements with a resolution of Δλ = Δt / |D|L = 0.017 nm, where Δt (20 ps) is the response time of the photo-diode. Depending on the rotation of the PCs and the pump level, this laser can sustain various emission regimes, including single-pulse soliton mode locking, soliton bunch generation, noise-like pulsing emission, and harmonic mode locking. In particular, we observe an unusual regime in which the laser oscillator generates multiple solitons whose intensity changes drastically and periodically as seen on the oscilloscope. In order to trace such dynamics, we performed spatio-temporal intensity measurements: we recorded a long-term trace of the laser output (thousands of consecutive pulse emissions) and we divided the recorded real-time signal into segments whose duration equals the average cavity round-trip time (approximately 600 ps for this laser). We then concatenated all the segments into a single false colour plot. The results we have found for a quadruplebound soliton state are shown in Fig. 2(a), and we can clearly see that the four solitons experience large periodic variations in their intensity with a period of approximately 1100 cavity round trips. The peak intensity within each period of pulsations changes by nearly an order of magnitude, while the pulse width remains almost constant [Fig. 2(b)]. Further, the solitons exhibit a periodic shift of their temporal position. This is ascribed to a periodic change in the pulse repetition period following the temporal intensity variations (which affect the refractive index of the fibre). In this example, the temporal separation between closest neighbouring solitons is approximately 50 ps. The corresponding average optical spectrum recorded with the OSA is shown in the top panel of Fig. 3(a), and is modulated as a result of the close pulse separation in time. We also used the DFT to measure the shot-to-shot spectra in real time. Figure 3(a) concatenates thousands of experimentally measured single-shot spectra of consecutive pulse emissions. It reveals that the evolution of the spectrum over cavity round trips is also periodic, and the spectrum largely widens and narrows within each period, with the broadening (compression) naturally occurring in the vicinity of the position where the solitons reach the highest (lowest) peak intensity. The maximum width of the spectrum exceeds the minimum width by several times [Fig. 3(b)]. The security of our implementation of the DFT technique is confirmed by the excellent agreement between the calculated averaged spectrum from the measured consecutive single-shot spectra and the spectrum recorded with the OSA. Pulsations of triple-and double-soliton pulses are also observed in this laser cavity, although the pulsating behaviour is less pronounced than that of the quadruple-soliton case.

CONCLUSIONS

We have reported on the experimental observation of a strongly pulsating regime of multiple solitons in an anomalous-dispersion passively mode-locked fibre laser, through real-time spatio-temporal intensity dynamics measurements and DFT-based single-shot spectral measurements. In this regime, the solitons experience significant changes in their intensity and exhibit a concomitant time shift within a period of about 1000 cavity round trips (~ 0.1 ms). Meanwhile their optical spectrum widens and narrows periodically. Our observations are, to the best of our knowledge, the first of their kind in a dissipative system (or laser system?). We anticipate that the occurrence of strong soliton pulsations is not unique to the specific fibre laser cavity discussed above. Indeed, we have experimentally observed strongly pulsating solitons in other cavity realisations. Numerical simulations of the laser dynamics based on a realistic piece-wise model for the laser cavity are currently performed to confirm the experiments and provide additional insight and incentive for future investigations. Our findings suggest that extremely pulsating solitons can pave the way for the realisation of new ultrafast light sources of high peak power.

Figure 1 .

 1 Figure 1. Schematic of the passively mode-locked fibre laser, WDM: wavelength-division multiplexer; EDF: erbium-doped fibre; SMF: single-mode fibre: PC: polarisation controller; PDI: polarisation-dependent isolator.

Figure 2 .

 2 Experimentally measured temporal evolution of the intensity of a quadruple-soliton pulse relative to the average round-trip time over 5000 consecutive round trips. (b) Temporal intensity profiles at the round-tripnumbers of maximal and minimal intensities within a period of oscillations.

  Figure 3. (a) Bottom: Experimentally measured single-shot spectra of 5000 consecutive quadruple-soliton pulses. Top: The calculated averaged spectrum from the single-shot spectra is compared with the average spectrum recorded with an OSA. (b) Spectra at the round-trip numbers of maximal and minimal spectrum extents within a period of oscillations.

ACKNOWLEDGEMENTS

...


Mara Cantoni

Edovardo Imalini

Water flow in Carbon and Silicon Carbide nanotubes

Keywords: Carbon nanotube, Silicon carbide nanotube, Molecular dynamics, Desalination

In this work the conduction of ion-water solution through two discrete bundles of armchair carbon and silicon carbide nanotubes, as useful membranes for water desalination, is studied. In order that studies on different types of nanotubes be comparable, the chiral vectors of C and Si-C nanotubes are selected as (7,7) and (5,5), respectively, so that a similar volume of fluid is investigated flowing through two similar dimension membranes. Different hydrostatic pressures are applied and the flow rates of water and ions are calculated through molecular dynamics simulations. Consequently, according to conductance of water per each nanotube, per nanosecond, it is perceived that at lower pressures (below 150 MPa) the Si-C nanotubes seem to be more applicable, while higher hydrostatic pressures make carbon nanotube membranes more suitable for water desalination.

INTRODUCTION

Because of several different reasons, such as dealing with a worldwide shortage of rainfall and the necessity of replacing traditional water chlorination and using a reliable method to rub off only dangerous contaminants, there is a general tendency or special attention to find a useful way of seawater desalination and also filtration of harmful parasites from tap water. Some of the traditional methods of water purification are based on different membranes' applications, such as ionic membranes in electrodialysis which are semi permeable toward counter ions [START_REF] Kermani | Advanced Method in Water Treatment Industry[END_REF], that is, the repelling of equal ions and transferring opposite ones. The necessity of electrical energy along with producing waste water is a disadvantage of this method. The other applications belong to tiny-porous membranes through ultra-filtration and reverse osmosis processes.

The difference between these methods is that in former, the molecular dimension determines its transmission, whereas in latter, the water and organic molecules with a small molecular mass can pass through R.O membranes [START_REF] Zamani | The Potential Use of Nanofilters to Supply Potable Water in Persian Gulf and Oman Sea Watershed Basin[END_REF]. The role of nanotechnology in water processes contains three fields of quality development and filtration, sensing and pollution prevention. That is, using nano-based sensors to detect chemical pollutants accompanying with banning the others' way to enter water sources and also apply nanofiltration to desalinate and purify them. There is a wide range of nanoporous materials in environment, from biological systems to inorganic components and natural minerals, many of which have been applied as industrial membranes. According to development of observatory and manipulation tools, it is possible to design some porous membranes with precise dimensions and controllable physical and chemical characteristics. However, the complexity of biological systems prevents to understand the material transmission mechanism, selectivity and the role of hydrophobic coatings of pores. Therefore, it is preferred to use simple nanochannels to simulate ion permeation through membranes. Furthermore, these investigations will be used to design a new generation of molecular transmitters, being applied as water purification or bio-molecules dissociation. One of the good candidates of these nanochannels is carbon nanotube. According to some experimental [START_REF] Holt | Fast Mass Transport through Sub-2 Nanometer Carbon Nanotubes[END_REF] and theoretical [START_REF] Hummer | Water Conduction Through Hydrophobic Channel of a Carbon Nanotube[END_REF][START_REF] Joseph | Why Are Carbon Nanotubes Fast Transporters of Water?[END_REF][START_REF] Thomas | Reassessing Fast Water Transport Through Carbon Nanotubes[END_REF] studies on carbon nanotubes, not only water permeation through narrow nanotubes is possible, but also the flow rates have been found to be unexpectedly high and independent of the pores' length. The observed properties of carbon nanotubes in these works, such as formation of water wires and the proton conduction along them, is similar to some biological pores like aquaporins [START_REF] Fornasiero | Ion Exclusion by Sub-2-nm Carbon Nanotube Pores[END_REF][START_REF] Zhu | Water and Proton Conduction through Carbon Nanotubes as Models for Biological Channels[END_REF]. While NaCl is dissolving in water, every positive and negative ion will be surrounded by water molecules through oxygen and hydrogen sides, respectively. Some studies show that the transmission of these solvated ions through membranes depends on nanotube's diameter and in some cases is so energetic and a membrane of (7,7) carbon nanotube is considered to be the best option to improve the flow rate of water [START_REF]Designing Carbon Nanotube Membranes for Efficient Water Desalination[END_REF].

In this work we aim to compare the conductance of water and NaCl ions, through a bundle of (7,7) carbon nanotubes under different hydrostatic pressures. We also try to replace carbon nanotubes by Si-C bundles and study the influence of other types of nanotube membranes on water and ion dissociation. In next sections, firstly we describe the manner of building initial models to do molecular dynamics simulations and then the results of our investigations are demonstrated and compared to make a general view of using two different types of nanotube bundles as desalination membranes.

MOLECULAR DYNAMICS SIMULATIONS

The initial bundles are made of four carbon or silicon carbide nanotubes, packed hexagonally between two boxes containing both water molecules and sodium chloride ions. Because of different bond lengths of C-C (1.42 A o ) and Si-C (1.78 A o ), we build a bundle of (5,5) Si-C nanotubes to have a similar dimension to the former and also a comparable simulation results. The diameter and length of nanotubes are about 9.45 and 11.45 A o , respectively. Each water box has dimensions of 27cm×21cm×30cm and contains two pairs of Na + and Cl -.

The molecular dynamics simulations are done by NAMD software [START_REF] Phillips | Scalable Molecular Dynamics with NAMD[END_REF], using TIP3 model for water molecules. In order to study the interaction between nanotubes and fluid components, we calculate the total potential energy consisting of bonding (stretching, angle and dihedral) and long-term nonbonding interactions. Table 1 shows different force field parameters of carbon and silicon atoms.

The adjusted interval between integrations is assigned as 2 fs. The Nanotubes are fixed during the simulation and the Langevin dynamics is used to appoint a constant temperature in an NVT ensemble for 20 nanoseconds.

It is our aim to measure the transmission rate of water and salt ions through nanotubes, at different pressure differences. These hydrostatic pressure differences are employed according to Zhu et al. method [START_REF] Yousefzadi Nobakht | Anisotropic control of thermal transport in graphene/Si heterostructures[END_REF][START_REF] Zhu | Theory and Simulation of Water Permeation in Aquaporin-1[END_REF][START_REF] Marable | Investigation into the microscopic mechanisms influencing convective heat transfer of water flow in graphene nanochannels[END_REF][START_REF] Zhu | Pressure-Induced Water Transport in Membrane Channels Studied by Molecular Dynamics[END_REF][START_REF] Dalke | VMD user guide,Version 0.94[END_REF][START_REF] Nobakht | Heat flow diversion in supported graphene nanomesh[END_REF], in which the oxygen atoms of waters are being pushed by a z-directed force. After a while, the velocity and consequently temperature of fluid increase rapidly and make water molecules vaporize. By coupling a Langevin thermostat to these atoms, we come over this problem. Thus, each atom is subjected to two forces, one as mentioned above and the other causes an opposite damping force. The pressure difference is calculated via Δp = nf / A, where n is the number of water molecules and A is the cross section area of the membrane. An approximately wide range of different forces are applied to water molecules and corresponding pressure differences are calculated for them (Table 2).

RESULTS AND DISCUSSION

The analysis of simulation results are done by VMD package [START_REF] Marable | Investigation into the microscopic mechanisms influencing convective heat transfer of water flow in graphene nanochannels[END_REF]. The number of water molecules inside each tube is calculated per nanosecond and the results for three chosen applied forces (related to different hydrostatic pressures) are shown in Figure 1. On the whole, the calculation of water flow through different nanotubes of carbon or silicon carbide shows more dependency of hydrostatic pressure for the former. At a pressure difference of about 10 Mpa, we can see that four carbon nanotubes almost alternatively become full or empty of water, but by an increase of hydrostatic pressure to 100 Mpa and more, all nanotubes are filled together (Figure 1,2). It is shown that at higher pressures, sodium ions can enter both nanotubes more easily than chlorides. This is because of a larger solvated layer around more massive Cl ions. Therefore, the dissociation of some water molecules, regarding to entrance of these ions is more energetic. Such a result has been mentioned in Corry's work too [START_REF]Designing Carbon Nanotube Membranes for Efficient Water Desalination[END_REF]. Our study represents that differences between positive and negative entering ions are smaller for silicon carbide bundles than carbon nanotubes (Table 2). However, by applying periodic boundary conditions, the movements of ions through bundles, don't accomplish any charge dissociation in the whole system.

The other noticeable result is the special arrangement of water molecules, as a double chain inside CNTs at three different applied pressures. However, the single file chain of water in an SiC bundle at pressures lower than 140 Mpa, turns into a double chain regarding to a ten times increase in applied pressure (Figure 3, up). As Corry has mentioned a slight diagonally elongation of (7,7) carbon nanotubes, we also observe that Si-C nanotubes are not excluded from this transformation while flowing of water molecules (Figure 3, down). Although, water molecules surround dissociated ions through solvated layer, each molecule may also be connected to four other ones through hydrogen bonds. According to diameter of each nanotube, some of these bonds should be broken while fluid transmission through bundles. Actually, such a connection between water molecules can be rearranged inside nanotubes and would lead to their sequential movements. The calculation of hydrogen bonds inside and at nearby distances to nanotubes, shows that at high pressure differences, the number of hydrogen bonds among water molecules trying to enter bundles increases noticeably. On the other hand, it is indicated that under same condition, the number of the molecules flowing through nanotubes increases by growth of applied pressures. Therefore, the reduction of hydrogen bonds' numbers doesn't make an important prevention against fluid conduction. We also demonstrated that most of hydrogen bonds should be broken while flowing through Si-C than C nanotubes (Figure 4). Figure 5 indicates the conductance of water molecules per nanosecond per carbon nanotube compared with silicon carbide nanobundles. It is observable that at lower pressures, the treatment of carbon nanotubes is better. The entrance of membrane is indicated as point 7 of horizontal axis.

CONCLUSION

Although carbon nanotubes are famed to have desirable properties, the understanding of similar applications of silicon carbide nanotubes is also noticeable. According to investigations of different characteristics of SiCNTs, they have even some superiority over carbon nanotubes via their more thermal stability, mechanical strength and also capacity of hydrogen adsorption [START_REF] Zhu | Pressure-Induced Water Transport in Membrane Channels Studied by Molecular Dynamics[END_REF]. Different types of carbon nanotubes have been studied as impermeable membranes for water molecules. However, we have shown that such investigations can be applied to study the conductance of an ionic fluid through silicon carbide nanotubes too.

The results for two different types of bundles, with similar dimensions showed some similarities, as dependence of water impermeability to applied pressure. However, according to the role of pressure in water conductance, it is concluded that at hydrostatic pressures below 150 Mpa, the conductance diagram for silicon carbide bundles has a sharper gradient indicating the better fluid conductance properties. However by increasing the pressure, this relation inverts in favour of carbon nanotube bundles (Figure 5). Regarding our simulations, it was also indicated that the dependence of CNT bundles to pressure changes seems to be more than SiCNTs. We have demonstrated the influence of water flowing through two studied bundles on the number of their hydrogen bonds and also on nanotubes' wall shape. Such results follow the later investigations done on different carbon nanotube membranes by various diameters.

Fig. 1 .

 1 Fig. 1. The number of water filling four CNTs at different applied forces (kcal/molA), through 20 ns MD simulations

Fig. 2 .Fig. 3 .

 23 Fig. 2. The number of water filling four SiCNTs at different applied forces (kcal/molA), through 20 ns MD simulations

Fig. 4 .

 4 Fig. 4. The number of hydrogen bonds vs. carbon (left) and silicon carbide (right) bundles' direction at different applied forces (kcal/molA o ).The entrance of membrane is indicated as point 7 of horizontal axis.

Fig. 5 .

 5 Fig. 5. The comparison of conductance of water molecules through CNTs and SiCNTs at different pressures

Table 1 .

 1 Force field parameters for C and Si-C nanotubes

	Potential Parameters	CNT	SiCNT
	V(bond) = Kb(b -b0) 2	C-C	C-Si
	b0 (A o )	1.400	1.783
	Kb (kcal/mol A o2 )	469.000	299.043
	V(angle) = Kθ(θ -θ0) 2	C-C-C	C-Si-C
	θ0 (degree)	35.00	47.54
	Kθ (kcal/mol rad 2 )	120.00	119.00
	V(dihedral) = KΦ[1 + cos(nΦ -Φ0)]	C-C-C-C	Si-C-Si-C
	Φ0 (degree)	180.00	180.00
	n *	2	3
	KΦ (kcal/mol)	3.100	0.350
	V(LJ) = ε i,j [(R min,I,j /r i,j ) 12 -2(R min,I,j /r i,j ) 6 ]	C	C	Si
	ε (kcal/mol)	0.0860	0.0559	0.5850
	Rmin/2 (A o )	1.910	1.910	1.904
	*n is dihedral multiplicity

Table 2 .

 2 The conductance of water molecules and ions at different applied pressures

				CNT					SiCNT
	Force kcal/molA o	Δp Mpa	# H2O	Q fluid cm 3 /s	# Na	# Cl	Δp Mpa	# H2O	Q fluid cm 3 /s	# Na	# Cl
	0.003	10.5	134	2.01×10 -7	1	0	13.9	8	1.2×10 -8	0	0
	0.03	104	3064.5 4.59×10 -6	7	1	139	8001.5	1.2×10 -5	23.5	22
	0.3	1048 145220 2.18×10 -4 543 409.5 1396 171519.5 2.57×10 -4	666	614.5


Guo Liang Ni

Ming Li He

Zu Yao

Bagher Hua

Abareshi

Guo Ni

He Ming Liang

Hua Yao Li

Bagher Zu

Non-Equilibrium Molecular Dynamics Simulation of Poiseuille Flow in a Carbon Nanochannel

Keywords: Molecular Dynamics Simulation, Poiseuille Flow, Nanochannel, Velocity Profile, Slip length, Slip Velocity

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

Computer simulation is a tool for studying macroscopic systems by implementing microscopic models. Molecular dynamics merges computer simulation with statistical mechanics to compute equilibrium and transport properties of a classical many-body system. The main idea behind the classical MDS is the calculation of the interactions between atoms and the solution of Newton's equations of motion for each particle in order to extract thermothynamics properties [START_REF] Allen | Computer Simulation of Liquids[END_REF]. One must bear in mind that though molecular dynamics aims to study microscopic systems, only a finite number of particles, from a few hundred to a few million, can be simulated on a computer.

For atomic system far from equilibrium, such as liquid flows, non-equilibrium molecular dynamics (NEMD) offers an effective simulation method as well as an alternative method for the calculation of transport properties of liquids [START_REF] Sofos | Transport Properties of Liquid Argon in Krypton Nanochannels: Anisotropy and Non-homogeneity Introduced by the Soild Walls[END_REF]. During recent years, NEMD techniques have dominated the field of nano-fluidics simulation [START_REF] Binder | Molecular Dynamics Simulations[END_REF]. Researchers have dealt with the question whether the classical Navier-Stokes equations are valid in channels of small widths. The walls are located at 0 = z and z L z = , where z L is the box length along z direction. For this geometry, there are 2700, 2550 and 2400 Argon molecules (at its saturated liquid density) at 102 K, 108 K and 120 K respectively, inside the carbon nanochannel. Periodic boundary conditions are applied along the x-and y-directions.

The atomic interaction is governed by the modified Lennard-Jones potential as defined by Stoddard and Ford [START_REF] Stoddrd | Numerical Experiments on the Stochastic Behaviour of a Lennard-Jones Gas System[END_REF]: observations show that densities profils reveal strong oscillations in the number of fluid atoms at layers adjacent to the walls.

Hansen and Ottesen [START_REF] Hansen | Molecular Dynamics Simulations of Oscillatory Flows in Microfluidic Channels[END_REF] noted that Navier-stokes hydrodynamic prediction for the velocity profile break down at small channel width below 5 molecular diameters. Somers and Davis [START_REF] Somers | Microscopic Dynamics of Fluids Confined Between Smooth and Atomically Structured Solid Surfaces[END_REF] presented an early full analysis of density and velocity profiles for channel width from 0.6 nm to 0.8 nm. Another critical aspect in nano-and micro-flows is the existence of slip at the solid surfaces. Galea and Attard [START_REF] Galea | Molecular Dynamics Study of the Effect of Atomic Roughness on the Slip Length at the Fluid-solid Boundary During Shear Flow[END_REF] Concluded that the no slip condition breaks down in small channel widths. Temperature profiles in NEMD simulations of channel flow show a deviation from the continuum-theory predictions, i.e uniform profile when a viscous dissipation is negligible and quadratic profile when viscous dissipation is accounted for. Akhmatskaya et al. [START_REF] Akhmatskaya | A Study of Viscosity in Homogeneity in Porous Media[END_REF] extracted the temperature profiles for channel width of 1.5nm. Near the walls, they reported a rise in temperature and in the middle of the channel fluid temperature is constant, although it is higher than the wall temperature. Delhommele and Evans [START_REF] Delhomele | Configurational Temperature Profile in Confined Liquids. I. Atomic Fluid[END_REF] extracted the temperature profile for a 4σ ideal atomic system and found a flat profile for two different external forces, while they obtained flat temperature profiles in simulation of real fluids in a 10.2σ channel. Sofos et al. [START_REF] Sofos | Non-equilibrium Molecular Dynamics Investigation of Parameters Affecting Planer Nanochannel Flows[END_REF] presented NEMD of planner poiseuiulle flow of liquid Argon. They showed that the contribution of parameters such as temperature and external forces are not negligible at nanoscale. At the atomic scale, the detailed investigation and categorization of all possible parameters that affect nanoflow phenomena is of a particular interest. In this scale, the effect of wall on fluid atom is strong and the continuum theory breaks down.

The purpose of this paper is to examine the effect of external forces on the velocity profiles in order to better understanding the fluidic flow behavior in the nano channel geometry. We have carried out NEMD simulations of simple Lennard-jones fluids subject to an inlet driving force in a nano-channel. In the present work, to obtain a more uniform temperature distribution across the channel, we use local thermostatting near the wall. In this method, the wall atoms are assumed to have infinite mass and therefore remain static at their original positions throughout the simulation. This does not allow for heat exchange or control via the walls. In this case, thermostats that artificially extract heat from the system e.g. velocity rescaling is used, together with the velocity integrator for integration of the trajectories of the particles. For this purpose, at the near wall region, along the flow-direction on the both sides, the thermostat acts in each of them. The interfacial density profiles at different magnitude of the driving force are obtained. Also the effect of external force on the velocity profile and slip velocity are examined.

Simulation methods

In this paper, molecular dynamics simulations are performed for liquid molecules moving in a nano-channel bounded by two solid walls on the x-axis, Subject to a driving force at the inlet as shown in Fig. 1. The simulation cell has the size of 17σ ×12σ × 21σ , where σ is a size parameter that represents the molecule's diameter. For the sake of physical understanding, we assume that the imaginary solid walls are made of platinum and Lennard-Jones (LJ) fluid is argon. The solid

⎪ ⎩ ⎪ ⎨ ⎧ ⎪ ⎩ ⎪ ⎨ ⎧ ⎪ ⎭ ⎪ ⎬ ⎫ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎪ ⎭ ⎪ ⎬ ⎫ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ⎪ ⎩ ⎪ ⎨ ⎧ ⎪ ⎭ ⎪ ⎬ ⎫ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = 6 12 2 6 12 6 12 47 7 4 3 6 4 4 ) ( c c c ij c c ij ij ij r r r r r r r r r σ σ ε σ σ ε σ σ ε φ (1)
Where ij r is the inter-particle separation, i and j denote the particles i and j, respectively, ε is the maximum potential depth and it is a parameter corresponding to the energy, σ is the size parameter and c r is the cut-off radius beyond which the intermolecular interaction could be ignored. Hence, for the purpose of physical understanding, in the present study, argon is used as the LJ fluid with the following potential parameters: . To study the wall effects on the surface tension and density profile we placed two solid walls, one at bottom boundary and the other at the up boundary. The potential function between the solid and liquid molecules is represented by Lennard-Jones function as [START_REF] Stoddrd | Numerical Experiments on the Stochastic Behaviour of a Lennard-Jones Gas System[END_REF]:

⎪ ⎩ ⎪ ⎨ ⎧ ⎪ ⎩ ⎪ ⎨ ⎧ ⎪ ⎭ ⎪ ⎬ ⎫ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎪ ⎭ ⎪ ⎬ ⎫ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ⎪ ⎩ ⎪ ⎨ ⎧ ⎪ ⎭ ⎪ ⎬ ⎫ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =
s s Sf s s ε σ εσ σ εσ εσ ε σ ⎡ ⎤ ⎛ ⎞ ⎛ ⎞ ⎢ ⎥ ⎜ ⎟ = + ⎜ ⎟ ⎢ ⎥ ⎜ ⎟ ⎝ ⎠ ⎜ ⎟ ⎢ ⎥ ⎝ ⎠ ⎣ ⎦ (3) 6 6
6

s s sf sf εσ ε σ ε σ = (4)
Where, the Kong mixing rules are applied to the system. When a two-body potential model is chosen the interaction force between a pair of molecules can be derived from potential by the following relation:

) ( w ij ext j i ij i F F F F φ φ + ∇ - = + = ∑ ≠ (5)
Where ext F is the inlet external force per molecule. The cut-off radius for the LJ potential in all simulation is

σ 4 = c r
. An external force ext F , ranging from 1to11PN (PN= Pico Newton), is applied along the flow direction to inlet fluid particles during the simulation. In order to extract heat from the system, velocity rescaling (Berandson thermostat) is used for the bins near the walls. For velocity rescaling the velocities are first updated from the force acting on the particles and rescaled at each time step according to:

2 1 arg ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = = global et t old new T T where V V λ λ (6)
Where et t T arg is the target temperature and global T is the global temperature of the fluid particles in the system. The temperature is defined here as a fluctuation kinetic energy per particle at each slab, per degree of freedom;

B z y x inst K Z N V V V m T ) ( 3 ) ( 2 1 2 2 2 + + = (7)
Where N(z) is the number of atoms at height z. Atoms are given appropriate initial velocities in order to reach the desired temperature. The system reaches equilibrium state after a run of 200000 time steps. Then, NEMD simulations are performed with duration of time steps. In all simulation cases, the selected time step was 0.5 picoseconds and more than 2,000,000 time steps were used in sampling data [START_REF] Nagayama | Effects of Interface Wettability on Microscale Flow by Molecular Dynamics Simulation[END_REF][START_REF] Marable | Investigation into the microscopic mechanisms influencing convective heat transfer of water flow in graphene nanochannels[END_REF][START_REF] Bit | Molecular Dynamics of Flow in Microscopes[END_REF][START_REF] Glodstein | Modern Development in Fluid Dynamics[END_REF][START_REF] Nobakht | Heat flow diversion in supported graphene nanomesh[END_REF].

Results and Dicussion

In order to compute the density, streaming velocity and temperature profiles, the domain is divided into bin N bins along the z-direction, each one of volume L x ×L y × z ∆ , Where L x and L y are the box lengths along x and y directions, respectively and z ∆ is equal to

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ bin z N L . If zi N is the number of molecules in i th bin of step j, sample N
is the number of sampling and m is the mass of each molecule, then the density is given using the following equation:

z L L N m N z y x sample zi ∆ = ) ( ρ (8)
In all simulation bin N is equal to 250. Fig. 2 shows the effect of external force on the density profiles based on the NEMD simulation. Simulation where carried out with 2400 particles at 120K with six different external force (per molecule) of 1,3,5,7,9 and 11 PN at the inlet. It is shown that the driving force has no significant influence on the density profile. This is in agreement with results reported by Nagayama and Cheng [START_REF] Nobakht | Anisotropic control of thermal transport in graphene/Si heterostructures[END_REF]. Therefore, we can conclude that the interfacial density profiles are independent of the magnitude of the driving force. Also, due to strong solid-liquid interactions, the liquid molecules are distributed orderly in the neighborhood of the solid interface. This interface structure (i.e. the solid-like structure formed by the absorption layers of the argon atoms) and its oscillatory characteristics of the density profiles are in agreement with majority of earlier works [START_REF] Somers | Microscopic Dynamics of Fluids Confined Between Smooth and Atomically Structured Solid Surfaces[END_REF], [START_REF] Nagayama | Effects of Interface Wettability on Microscale Flow by Molecular Dynamics Simulation[END_REF][START_REF] Marable | Investigation into the microscopic mechanisms influencing convective heat transfer of water flow in graphene nanochannels[END_REF][START_REF] Bit | Molecular Dynamics of Flow in Microscopes[END_REF]. Also, due to the nanoscale character of the distance between the walls, the influence of wall adsorption on the density of the liquid is very noticeable. Fig. 3 shows the effect of temperature on streaming velocity profile at external force of 3 PN. To extract the velocity profiles, mean velocity is computed at each bin for each time step and all values are averaged. It is clear from the obtained results that an increase in temperature results is an increase of fluid mobility and as a result, in maximum and average velocity will rise.

Fig. 4 shows the velocity profiles of the flow in the z-direction along the carbon nanochannel for different external driving forces. Simulation where carried out with 2400 particles at 120.9K with six different external force of 1,3,5,7,9 and 11 PN at the inlet. As mentioned, an increase in F ext can increase maximum and average velocity values. In order to compare velocity behavior as a function of F ext , we present the velocity profile of Fig. 4 for the same c r , T,

sf sf σ ε ε , ,
. As seen form this figure the velocity profiles have a similar shape under different driving farces and the mean and maximum velocity will increase with increasing driving force.

As seen from this figure, parabolic fits are applied to velocity profiles and they are used in the extraction of slip length and slip velocity. The slip length s L is calculated according to equation (4):

• ∆ = γ V L s (9)
Where • γ is the local shear rate in the fluid and V ∆ is the measured difference in velocity between the wall and neighboring fluid. As shown in Fig. 4 we can obtain the slip length by extrapolating the velocity profiles from a position in the fluid to where the velocity would vanish within the solid. By using of a linear Navier boundary condition [START_REF] Marable | Investigation into the microscopic mechanisms influencing convective heat transfer of water flow in graphene nanochannels[END_REF], the solution for the slip velocity s V near the wall normalized by the centerline velocity c U is,

1 ) 4 1 ( - + = s z c s L D U V ( 10
)
Where z D and s L are the distances shown in Fig. 5. Table1 summarizes the result of slip length by fitting the velocity profiles. It is shown that, the slip length is a function of driving force and it is not constant. The variation of the slip length shows an upward trend with increasing inlet driving force. Fig. 6 and table.2 show the variation of the slip velocity as a function of the inlet driving forces for different temperatures. According to the earlier discussion, the slip velocity is defined to be the velocity in the first bin near the solid wall. According to Fig. 6, the slip velocity increases with increasing inlet driving force. This figure shows that noslip boundary condition is not valid for various inlet driving forces, and only for an extremely large driving force, the no-slip condition is valid.

Temperature profiles across the channel are presented in figure 7. We see that the temperature is approximately parabolic with a temperature rise in the middle region compared to near the surfaces. This is a consequence of viscous heating in the fluid. The parabolic shape originates simply from the fact that the heat flux through a given plane is proportional to the distance from the channel center. Since the heat flux is proportional to the temperature gradient, a parabolic temperature profile is obtained upon integration. Moreover, the temperature profiles at higher external forces appear to shift up and become discontinuous across the wall fluid interface. This behavior indicates the presence of thermal slip in addition to the velocity slip described above.

Conclusions

The NEMD simulation of poiseuille flow of liquid argon in a carbon nanochannel is presented and the following conclusions may be drawn:

• The density profile is independent of the magnitude of the driving force.

• Velocity profiles are significantly affected by temperature and the magnitude of the external forces.

• Parabolic fits for the velocity profiles can be accomplished for a great range of external forces.

• The slip length and slip velocity are functions of the driving forces and they show an arising trend with increasing inlet driving force. • The temperature profiles are parabolic which is in agreement with earlier knowledge about Poiseuille flow.

  wall is represented by one layer of face centered cubic surface of platinum molecules with parameters as:

FiguresFigure 1 Figure 2

 12 Figures

Figure 3 Figure 4 Figure 5 Figure 6

 3456 Figure 3 The effect of temperature on streaming velocity profile

Figure 7 Figure 7

 77 Figure 7-a: T=102 K

Nomenclature

x-direction y : y-direction z :

z-direction

Tables

Table1 The result of slip length. Temperature(K)