Tanti Kristanti
email: tanti.kristanti@inria.fr

Laurent Romary
email: laurent.romary@inria.fr

DeLFT and entity-fishing : Tools for CLEF HIPE 2020 Shared Task

Keywords: entity recognition, entity linking, machine learning, deep learning

This article presents an overview of approaches and results during our participation in the CLEF HIPE 2020 NERC-COARSE-LIT and EL-ONLY tasks for English and French. For these two tasks, we use two systems: 1) DeLFT, a Deep Learning framework for text processing; 2) entity-fishing, generic named entity recognition and disambiguation service deployed in the technical framework of INRIA.

Introduction

Named Entity Recognition (NER) refers to the task of identifying text spans that mention named entities and classifying them into predefined classes (e.g., person, location, organization). Whereas, Entity Linking (EL) refers to the task of detecting textual entity mentions and matching them to corresponding entries within knowledge bases (e.g., Wikipedia, Wikidata). Over the past few years, traditional machine learning-based (i.e., rule-based, unsupervised, and featurebased supervised learning) approaches have evolved into deep learning (DL) approaches, yielding state-of-the-art performances [START_REF] Habibi | Deep learning with word embeddings improves biomedical named entity recognition[END_REF][START_REF] Lample | Neural architectures for named entity recognition[END_REF][START_REF] Santos | Boosting named entity recognition with neural character embeddings[END_REF]. For our participation in the CLEF HIPE 2020 shared task, we use two different systems that implement non-neural machine learning (ML) and DL approaches.

In HIPE, a shared task dedicated to the evaluation of named entity (NE) processing on historical newspapers in French, German, and English [START_REF] Ehrmann | Overview of CLEF HIPE 2020: Named Entity Recognition and Linking on Historical Newspapers[END_REF], we participated in two different NERC-COARSE-LIT and EL-ONLY tasks by using two systems: DeLFT and entity-fishing. Deep Learning Framework for Text (DeLFT) is a framework for text processing, which re-implements standard state-of-the-art DL architectures. Meanwhile, entity-fishing is a generic named entity recognition and disambiguation (NERD) system, which applies supervised machine learning based on Random Forest and Gradient Tree Boosting exploiting various features.

Both DeLFT1 and entity-fishing2 are open-source systems under an Apache 2 license. Codes, models, and resources that are publicly available through the Github repository allow users and contributors, including us, to use existing services and models and to contribute to system and model improvements and tests. With the use of DeLFT, our goal is to re-build DL-based models for recognizing mentions within English and French HIPE historical corpus belonging to Person (pers), Location (LOC), Organization (ORG), Product (PROD), and Time (TIME) classes. Meanwhile, with entity-fishing service, we use the service to disambiguate provided mentions within French and English HIPE data against Wikidata entries.

Tools

This section provides a general description of the two systems we use, DeLFT and entity-fishing. For a better understanding of technical discussions, it is advisable to refer directly to their repositories and documentation.

DeLFT

Deep Learning Framework for Text (DeLFT) is an open-source framework for text processing, including sequence labeling (e.g., NE tagging) and text classification problems. This Keras and TensorFlow framework re-implements standard state-of-the-art DL architectures for text processing.

DeLFT supports many DL architectures (e.g., Bidirectional LSTMs and Conditional Random Fields [START_REF] Lample | Neural architectures for named entity recognition[END_REF], Bidirectional LSTM and Convolutional Neural Networks [START_REF] Chiu | Named entity recognition with bidirectional lstm-cnns[END_REF], Bidirectional Gated Recurrent Unit [START_REF] Peters | Semi-supervised sequence tagging with bidirectional language models[END_REF]) and contextualized embeddings (e.g., ELMo, BERT). For using the desired pre-trained word embeddings, we need to provide them from the source separately. DeLFT then loads and manages these embeddings by compiling at the very first access to be stored in a database.

entity-fishing

entity-fishing is a generic NERD system against Wikidata. Deployed as part of the French national infrastructure Huma-Num3 , the service provides a standardized interface, open and flexible architecture, allowing easy deployment, including in digital humanities contexts. Initiated in the context of the EU FP7 Cendari project from 2013 to 2016, entity-fishing aimed at setting up a digital research environment for historians of the medieval and WWI periods to access archival contents and acquire numerous assets or entities information [START_REF] Foppiano | entity-fishing: a DARIAH entity recognition and disambiguation service[END_REF].

In general, entity-fishing has three phases: language identification, mention recognition, and entity resolution. First, language identification is necessary for selecting appropriate utilities for text processing (e.g., tokenizer, sentence segmentation) and a specific Wikipedia from the knowledge base. Second, mention recognition has the responsibility to extract entity mentions from the input.

To support the generic nature, even though prepared with a set of recognizers, entity-fishing provides the possibility for users to extend with additional ones.

entity-fishing supports traditional mention extractors: named entity recognition, Wikipedia lookup, acronym extraction. For NER, entity-fishing uses grobidner. grobid-ner4 is a library for processing texts, extracting named entities, and classifying these entities into 27 classes (e.g., person, location, media, organization, period) using a Conditional Random Field (CRF) statistical model. Meanwhile, Wikipedia lookup is complementary to the machine learning NER approach. The lookup attempts to find all mentions that correspond to either a title or an anchor in Wikipedia using an N-gram-based matching approach. For the acronyms, entity-fishing treats them as mentions and uses the base for disambiguation. The resolved entity is then further propagated in the text for each occurrence of the acronym. The result of the mention recognition step is an aggregated list of objects containing raw values from the original text, their actual positions, and NER classes (within the 27 classes).

Lastly, entity resolution is the process of matching entity mentions to their corresponding Wikidata entries. The entity resolution has three stages: candidate generation, candidate ranking, candidate selector. In the candidate generation phase, each mention has a list of possible candidates for the disambiguation. Then, in the candidate ranking, each candidate is assigned a confidence score calculated as regression probability using various features.

Auxiliary Resources

We use external datasets and embeddings in addition to those provided by the HIPE organizers.

Datasets The HIPE corpus consists of training, dev, and test datasets for each task and language. However, since for English, HIPE does not provide the training data, we use a pre-trained CoNLL-2012 (based on Ontonotes 5.0) [START_REF] Pradhan | Conll-2012 shared task: Modeling multilingual unrestricted coreference in ontonotes[END_REF] model and test the model with the HIPE test data.

Moreover, motivated by the promising French model results published by DeLFT, we use the annotated [START_REF] Sagot | Annotation référentielle du Corpus Arboré de Paris 7 en entités nommées[END_REF] French TreeBank (FTB) corpus and the HIPE data to re-build and benchmark the NER French model. This French journalistic genre corpus from the year 1990 is the annotated 2007 version of the FTB treebank containing the span, the literal type, sometimes completed with a subtype, and Aleda unique identifier of each mention. They use seven basic classes: Person, Location, Organization, Company, Product, POI (Point of Interest), and FictionChar (fictional character). FTB corpus contains 11,636 manually annotated mentions with the distribution of 3,761 location names, 3,357 company names, 2,381 organization names, 2,025 person names, 67 product names, 29 fictional character names, and 15 POIs.

Word Embeddings

We use various static word embeddings: Global Vectors for Word Representation (GloVe) [START_REF] Pennington | Glove: Global vectors for word representation[END_REF], English fastText Common Crawl [START_REF] Bojanowski | Enriching word vectors with subword information[END_REF][START_REF] Mikolov | Advances in pretraining distributed word representations[END_REF], and French Wikipedia fastText. 5 We also use ELMo [START_REF] Peters | Deep contextualized word representations[END_REF] contextualized word representations for English6 and French7 . [START_REF] Lample | Neural architectures for named entity recognition[END_REF] 90.94 --Ma and Hovy (2016) [START_REF] Ma | End-to-end sequence labeling via bi-directional lstm-cnns-crf[END_REF] 91.21 --Chiu and Eric (2016) [START_REF] Chiu | Named entity recognition with bidirectional lstm-cnns[END_REF] 91.62 86.28 -Peters, et al. (2018) [START_REF] Peters | Deep contextualized word representations[END_REF] 92.22 --Devlin, et al. (2018) [START_REF] Devlin | Bert: Pre-training of deep bidirectional transformers for language understanding[END_REF] 92.80 -non neural achitectures Ratinov and Roth (2009) [START_REF] Ratinov | Design challenges and misconceptions in named entity recognition[END_REF] 90.80 --Passos, et al. (2014) [START_REF] Passos | Lexicon infused phrase embeddings for named entity resolution[END_REF] 90.90 82.30 -Luo, et al. (2015) [START_REF] Luo | Joint entity recognition and disambiguation[END_REF] 89.90 --Luo, et al. (2015) + linking [START_REF] Luo | Joint entity recognition and disambiguation[END_REF] 91.20 --

Benchmarking NER Models

Machine learning approaches have dominated NER, but the trend is towards neural network architectures that achieve state-of-the-art performances. For this reason, we compare several published NER systems as well as DeLFT pretrained models against various corpora (i.e., CoNLL-2003, CoNLL-2012, FTB) and present them in Table 1.

[18] non-neural machine learning system achieves a 90.80 F1-score on CoNLL-2003. [START_REF] Passos | Lexicon infused phrase embeddings for named entity resolution[END_REF] improves with 90.90 on CoNLL-2003 and 82.30 on Ontonotes 5.0. Although [START_REF] Luo | Joint entity recognition and disambiguation[END_REF] exceeds the previous achievements with their NERD system, which pushes the F1-score to 91.20. Nevertheless, their NER pure system reaches 89.90.

Meanwhile, for neural architectures, [START_REF] Lample | Neural architectures for named entity recognition[END_REF] reaches a 90.94 F1-score on CoNLL-2003, then [START_REF] Ma | End-to-end sequence labeling via bi-directional lstm-cnns-crf[END_REF] improves the results. [START_REF] Chiu | Named entity recognition with bidirectional lstm-cnns[END_REF] reports an F1-score of 91.62 on CoNLL-2003 and 86.28 on OntoNotes 5.0. [START_REF] Peters | Deep contextualized word representations[END_REF] ELMo enhanced bidirectional LSTM with a CRF layer (BiLSTM-CRF) achieves an averaged F1-score of 92.22 over five runs. [START_REF] Devlin | Bert: Pre-training of deep bidirectional transformers for language understanding[END_REF] has a competitive performance with state-of-the-art systems its BERT LARGE fine-tuning approach tested on CoNLL-2003 reaches 92.80.

DeLFT has reimplemented neural architectures for NER [3]. Table 1 presents reported best F1-scores over ten runs for the English model using CoNLL From these results, we learn that DL-based systems have better performance than conventional machine learning systems. The use of contextualized word embeddings within the BiLSTM-CRF architecture improves the scores. The results in the CoNLL-2003 column also show that ELMo-based models give better F1-score than BERT-based models.

Work Phases

In general, the HIPE shared task contains two tasks:

1. Named Entity Recognition and Classification (NERC): the recognition and classification of entity mentions with predefined high-level (i.e., pers, org, prod, loc, time), finer-grained, or nested entity classes. 2. Named Entity Linking (NEL): the task of matching identified entity mentions to Wikidata entries, with or without prior knowledge of mention types and boundaries.

Named Entity Recognition and Classification (NERC)

Although the English model built with the CoNLL-2003 dataset is promising, this model does not support the Time (Date) entities. Moreover, since HIPE does not provide training data for English, we use a CoNLL-2012 pre-trained model within the BiLSTM-CRF architecture, and ELMo contextualized word embeddings. For the French model, we enrich the French HIPE (i.e., the version 1.2 train and dev) dataset with annotated FTB data.

For training the models, we follow the default hyper-parameters8 as applied for other pre-trained sequence labeling models in DeLFT, except for the batch size and maximum epoch, we follow as indicates here. 9Challenges Combining data from different environments poses challenges, particularly with the reason of different NE class definitions as well as annotation guidelines. CoNLL-2012 define 18 classes. FTB corpus comes with seven NE classes. Meanwhile, HIPE uses five classes.

HIPE annotates absolute dates without months and hours, which confirms to the CoNLL-2012 DATE class. Furthermore, the HIPE Location (loc) entities suites with those belonging to CoNLL-2012 FAC (i.e., buildings, airports, highways, bridges), GPE (i.e., countries, cities, states), and LOCATION (i.e., non-GPE locations, mountain ranges, bodies of water) entities. It's also challenging to search the equivalence of the HIPE PROD entities, which we understand as media products since CoNLL-2012 classifies them in the ORG class.

Experiments We benchmarked the French NER trained with the HIPE data (i.e., train and dev v-1.2) only and the HIPE plus additional FTB data. The only HIPE model achieved an F1-score of 85.71 on the dev set. Meanwhile, the enriched model performs better with an increase of 3 scores into 88.46.

Named Entity Linking

For the NEL task, we use entity extraction and disambiguation services provided by entity-fishing. There are several ways to access these services; however, the most straightforward way is to use the service RESTful web services. 10First, we collect the text from the HIPE data. Then, we include this text as part of the JSON input query. The entity-fishing query processing service takes as input a JSON structured query and returns the JSON query enriched with a list of identified and, when possible, disambiguated entities. The JSON query format for the response file is identical to the input query. The client must respect the JSON query format, which is as follow:

Table 2 lists the best system, our system, and the baseline results for the NE-COARSE-LIT and EL-ONLY tasks.11 Our NER system performs worse than the L3i system. However, we perform better than the provided baseline, which is a CRF sequence classifier. We have an exception to the French NE-COARSE-LIT-strict result, which is slightly below the baseline F1-score.

It turns out that our EL system, especially for English, performs better than the L3i team and the aidalight-baseline, which corresponds to [START_REF] Nguyen | Aida-light: High-throughput named-entity disambiguation[END_REF]. Our French EL system is better than the L3i EL system in terms of recall but rather appalling in terms of precision.

Table 3 and Table 4 present our English and French NER and EL performance on the HIPE test data with detailed information on false positive and false negative numbers. Strict NER, which is a more demanding task, performs worse than fuzzy NER. Looking further at each class, we highlight that there are considerably misclassified PROD entities and thus contribute to numerous false negatives.

Lang Evaluation

Label P R F1 TP FP FN EN NEL-LIT-micro-fuzzy-@1 ALL 0.633 0.685 0.658 305 177 140 EN NEL-LIT-micro-fuzzy-relaxed-@1 ALL 0.633 0.685 0.658 305 177 140 EN NEL-LIT-micro-fuzzy-relaxed-@3 ALL 0.633 0.685 0.65 305 177 140 EN NEL-LIT-micro-fuzzy-relaxed-@5 ALL 0.633 0.685 0.658 305 177 140 FR NEL-LIT-micro-fuzzy-@1 ALL 0.585 0.65 0.616 1039 737 560 FR NEL-LIT-micro-fuzzy-relaxed-@1 ALL 0.604 0.67 0.635 1072 704 527 FR NEL-LIT-micro-fuzzy-relaxed-@3 ALL 0.604 0.67 0.635 1072 704 527 FR NEL-LIT-micro-fuzzy-relaxed-@5 ALL 0.604 0.67 0.635 1072 704 527

Conclusion

As our participation in the HIPE shared task, we highlight that the quantity and quality of data need are essential for the NERC and the NEL tasks. Further, although

  -2003 and CoNLL-2012 and the French model using the FTB corpus. The model trained with CoNLL-2003 within the BiLSTM-CRF architecture and GloVe word embedding, tested against the test set, achieves a 91.35 F1score. The result is improving with GloVe combined with ELMo. Within BERT architecture and the CRF activation layer for fine-tuning, the model achieves an average of 91.20 F1-score. The best F1-score on CoNLL-2003 is 93.09 when using both train and validation datasets within a BiLSTM-CRF architecture, coupled with GloVe and ELMo embeddings. Meanwhile, the CoNLL-2012-based model within the BiLSTM-CRF architecture and the fastText embedding achieves an F1-score of 87.01. The involvement of ELMo increases the score by 2 points to 89.01. The French model trained with the FTB corpus within the BiLSTM-CRF architecture and French Wikipedia fastText reaches an 87.45 F1-score. Meanwhile, with the use of French ELMo, the score is improving into 89.23.

Table 1 .

 1 Comparison of DeLFT NER models with various feature sets and other published systems.

	Model	CoNLL-2003 [20] Ontonotes 5.0 [17] FTB [19] F1-score
	DeLFT models [3]
	CoNLL-2003-BiLSTM-CRF + GloVe	91.35	-	-
	CoNLL-2003-BiLSTM-CRF + GloVe + ELMo	92.71	-	-
	CoNLL-2003-BiLSTM-CRF + GloVe + ELMo + valid set	93.09	-	-
	CoNLL-2003-BiLSTM-CNN-CRF + GloVe	91.07	-	-
	CoNLL-2003-BiLSTM-CNN-CRF + GloVe + ELMo	92.57	-	-
	CoNLL-2003-BiLSTM-CNN-CRF + GloVe + ELMo + valid set	93.04	-	-
	CoNLL-2003-BiLSTM-CNN + GloVe	89.47	-	-
	CoNLL-2003-BiLSTM-CNN + GloVe + ELMo	92.00	-	-
	CoNLL-2003-BiLSTM-CNN + GloVe + ELMo + valid set	92.16	-	-
	CoNLL-2003-BiGRU-CRF + GloVe	90.72	-	-
	CoNLL-2003-BiGRU-CRF + GloVe + ELMo	92.44	-	-
	CoNLL-2003-BiGRU-CRF + GloVe + ELMo + valid set	92.71	-	-
	CoNLL-2003-BERT-base	90.90	-	-
	CoNLL-2003-BERT-base + CRF	91.20	-	-
	CoNLL-2012-BiLSTM-CRF + fastText	-	87.01	-
	CoNLL-2012-BiLSTM-CRF + fastText + ELMo	-	89.01	-
	FTB-BiLSTM-CRF + fastText	-	-	87.45
	FTB-BiLSTM-CRF + fastText + ELMo	-	-	89.23
	neural achitectures
	Lample, et al. (2016)

Table 3 .

 3 NERC-COARSE-LIT results on the HIPE test data. EN NE-COARSE-LIT-micro-fuzzy ALL 0.568 0.746 0.645 335 255 114 EN NE-COARSE-LIT-micro-strict ALL 0.461 0.606 0.524 272 318 177 FR NE-COARSE-LIT-micro-fuzzy ALL 0.755 0.842 0.796 1347 438 253 FR NE-COARSE-LIT-micro-strict ALL 0.605 0.675 0.638 1080 705 520

	Lang Evaluation	Label P	R	F1 TP FP FN

Table 4 .

 4 EL-ONLY-LIT results.

https://github.com/kermitt2/delft

https://github.com/kermitt2/entity-fishing

https://www.huma-num.fr/

https://github.com/kermitt2/grobid-ner

https://s3-us-west-1.amazonaws.com/fasttext-vectors/wiki.fr.vec

https://s3-us-west-2.amazonaws.com/allennlp/models/ELMo/

https://traces1.inria.fr/oscar/files/models/cc/fr.zip

https://github.com/kermitt2/delft/blob/master/delft/sequenceLabelling/config.py

https://github.com/kermitt2/delft/blob/master/nerTagger.py

https://nerd.readthedocs.io/en/latest/restAPI.html

https://github.com/impresso/CLEF-HIPE-2020/blob/master/evaluationresults/ranking_summary_final.md

Acknowledgements We thank the anonymous reviewers for their insightful comments.

{ "text": "The text to be processed.", "shortText": "term1 term2 ...", "termVector": [ { "term": "term1", "score": 0.3 }, { "term": "term2", "score": 0.1 } ], "language": { "lang": "en" }, "entities": [], "mentions": ["ner","wikipedia"], "nbest": 0, "sentence": false, "customisation": "generic", "processSentence": [], "structure": "grobid" } Table 2. NERC-COARSE-LIT and EL-ONLY results compared to the best system and the baseline. Our results are highlighted. NEL-LIT-micro-fuzzy-@1 0.593 0.593 0.593 EN aidalight-baseline NEL-LIT-micro-fuzzy-@1 0.506 0.506 0.506 FR L3i

Lang Team

NEL-LIT-micro-fuzzy-@1 0.64 0.638 0.639 FR Inria-DeLFT NEL-LIT-micro-fuzzy-@1 0.585 0.65 0.616 FR aidalight-baseline NEL-LIT-micro-fuzzy-@1 0.502 0.495 0.498

DeLFT and entity-fishing achieve good F1-scores, their performance is quite sensitive to noise data.


Antony Eastmond, ed., Viewing Inscriptions in the Late Antique and Medieval World. New York: Cambridge University Press, 2015. Pp. 275, ills. 73 b/w. ISBN 978-1-107-09241-9.

As the title indicates, Viewing Inscriptions in the Late Antique and Medieval World is about the nonverbal visual characteristics of late antique and medieval inscriptions. Unlike previous studies that typically concentrate on reading and the semantic content of writing, this volume focuses on the materiality of inscriptions and their formal, artistic and spatial strategies of communication. The broad chronological and geographical scope, from Achaemenid Persia to fourteenthcentury Italy, challenges traditional disciplinary boundaries and engages in a cross-cultural comparison on the role of inscriptions in forging and conveying distinct social, cultural and religious identities. By bringing together a multitude of approaches, this collection of articles not only raises awareness of the commonalities in the usage of writing as art across time and space, but it offers an inspiring array of methods in its quest to elucidate the extraordinary variety of media and contexts in which inscriptions occur and the motivations underlying their production, modification and use. This is an important contribution to the exploration of the multidimensional quality of inscriptions in the ancient and medieval world, pertinent above all in light of the widespread popularity of the use of writing, monumental or other. Antony Eastmond's introduction offers a succinct overview of the three major threads that run through the different case studies in this volume and that control the function and meaning of inscriptions. Central to all discussions is the issue of legibility and readability, which is closely allied with its formal qualities and the typeset of the script as well as with the type of language and the question of literacy. Together, these factors establish a particular relationship with the reader/viewer and determine how an inscription is primarily confronted. Second, as material entities, inscriptions interact with and fundamentally shape their immediate physical environment. Due to their intrinsically performative nature, inscriptions thus affect how an object or monument is perceived and experienced. Finally, the functionality and performativity of inscriptions are deeply embedded in tradition and rely on the expectations and imaginations of the communities which they serve. Inscriptions react to what came before and create a new and distinctive use of writing through adaptation. This is why inscriptions are best considered within the longue durée of ancient epigraphy, which is exactly what this volume proposes to do.

The eleven articles explore an extraordinary diversity of contexts and types of writing. They range from royal inscriptions and the creation of national identities in the ancient Iranian world, Norman Sicily or thirteenth-century Spain to unauthorised early Christian graffiti and informal craftsmen's signatures in medieval Islamic art. The majority of articles discuss the carefully orchestrated official decorative programmes meant to strengthen cultural, religious and/or political associations in a variety of contexts like the façades of the tenth-century cathedral of Kumurdo in Georgia, pseudo-Arabic inscriptions at Hosios Loukas in the eleventh century, the Qur'anic inscriptions of the thirteenth-century Qaratay Madrasa in the Seljuk capital of Konya or monastic inscriptions in fourteenthcentury Armenia. Others examine the use and modifications of inscriptions to invent, corroborate or erase history as in the case of the monumental inscriptions of ninth-and tenth-century North Africa or early fourteenth-century Genoa.

Exemplary for the diverse themes and topics that underlie this volume as a whole is Matthew Canepa's "Inscriptions, Royal Spaces and Iranian Identity: Epigraphic Practices in Persia and the Ancient Iranian World" (Chapter 1). It outlines the broad chronological and cultural trends of appropriation, integration, departure and creative re-invention, by tracing Sasanian and early Islamic epigraphic practices back to Achaemenid and Hellenistic inscriptional conventions. The Bisotun inscription of Darius I (r. 522-486 BCE), for instance, carved into the bare rock high up on the face of a cliff in three different languages, exemplifies the issues of accessibility, legibility and readability, and illustrates the extent to which an inscription marks and shapes its natural environment and its perception. Darius I's monumental inscriptions provide the template for the manipulation of history and the proclamation of kingship in later Iranian dynasties. The structure and themes of late antique Sasanian inscriptions correspond remarkably close to those of their Achaemenid predecessors even though language and script had since changed. Sasanian Persia is a typical example of how inscriptions engage with earlier epigraphic practices and how they conveyed meaning by association.

To communicate meaning through formal qualities is particularly relevant in relation to multilingual inscriptions. They typically signify the attempt to appropriate the visual culture of the defeated communities and are often reflective of multi-ethnic and/or multi-confessional societies. The systematic use of bilingual and trilingual texts by the Norman kings of Sicily is a case in point. As Jeremy Johns argues in chapter six, the Arabic inscriptions in the Cappella Palatina are hardly legible and operate not as texts per se but rather as an index to the Norman monarchy and the ideology of kingship. Tom Nickson identifies similar trends in the use of multilingual epitaphs (Latin, Castilian, Arabic, Hebrew) of King Fernando III of Castile-Léon (Chapter 8). Here, the multitude of languages does not so much reflect the cosmopolitan character of thirteenth-century Castile as it is an expression of royal power and wisdom.

The choice of language and script is evidently important. Whereas the Sasanians seem to have decided in favour of their vernacular as the preferred language for monumental inscriptions (Chapter 1), in the Seljuk Qaratay Madrasa in Konya, the Qur'anic quotations were written in Arabic that was not the everyday language spoken at the time (Chapter 7). Scott Redford draws attention to the shift in the use of the script style from legible cursive script at the entrance of the Qaratay Madrasa to an interlaced kufic, hard to decipher, at the base of the dome. This deliberate use and placement of the inscriptions in conjunction with the overall decorative and architectural programme alludes, according to Redford, to different levels of knowledge and the idea of divine enlightenment with a profoundly pedagogical purpose. Kuficesque writing was similarly manipulated to evoke a theological meaning in the fourteenth-century decoration on the façade of the monastery of Noravank in Armenia (Chapter 9). Ioanna Rapti discusses how the aesthetic and semantic qualities of the script of its tympanum convey the mystery of the Logos and the divine essence. This exploitation of inscriptions is reminiscent of what Alicia Walker describes as the 'iconic use of writing' (Chapter 5). Walker notes that pseudo-Arabic at Hosios Loukas was deliberately placed so as to guide the visitor around the monastic complex and to highlight areas of particular importance, thus controlling the pilgrim's experience of the site. She argues that the pseudo-Arabic decoration in the tenth-century north church was at once a visual statement of the Byzantine triumph over Islam and of an apotropaic function. In the eleventh century, pseudo-Arabic took on a different meaning, alluding to the Christian loci sancti in the Holy Land now under Islamic rule. A parallel case of 'textual icons' is presented by Antony Eastmond in chapter four on architectural inscriptions in medieval Georgia. Here, the text was subordinate to its visuality as part of a larger decorative programme. Meaning derived primarily from its formal characteristics evocative of the mnemonic potential of Orthodox icons.

The construction of historical memory is the central topic of Stefania Gerevini's "Written in Stone: Civic Memory and Monumental Writing in the Cathedral of San Lorenzo in Genoa" (Chapter 10). Textual and visual elements of the inscription in the nave of the cathedral of San Lorenzo work in tandem to reinforce civic identity and social unity. The epigraphs bestowed authority and truth-value to the myth of the foundation of the city of Genoa by juxtaposing the myth with the dedicatory inscription and thereby transforming it into history 'written in stone'. A different type of re-writing history is considered by Jonathan Bloom in chapter three. The repeated erasure and alteration of architectural inscriptions in Aghlabid and Fatimid north Africa functioned as a damnatio memoriae. The overt blank spaces left behind draw attention to the modifications and acted as constant reminders of political change and the condemnation of previous regimes.

Informal inscriptions such as graffiti can also have a transformative effect on a monument by adding markers of a personal and intimate nature. Ann Marie Yasin explores the performative and commemorative function of graffiti in early Christian contexts (Chapter 2) that reflect and shape the experience of sacred places. Graffiti, she argues, allow an individual to become a permanent part of a holy site and its community. The surviving evidence suggests that graffiti were often concentrated around entrances and thresholds, that they inspired plagiarism and thus delineate the sacred topography and sites of popular devotion. Informal inscriptions take centre stage also in Sheila Blair's contribution on craftsmen's signatures in medieval Islamic art (Chapter 11). Casual signatures on ivory boxes from Umayyad Spain, for example, reflect not only workshop practices, but above all the craftsman's status and changes thereof. The placement of informal signatures, whether in direct association with the foundation inscription, in an inconspicuous place or literally under the very foot of the patron signalled hierarchical structures, in which the artisan usually occupied the lowest order. As always, these informal signatures form part of a larger ensemble and the context is important. This brings me back to one of the book's fundamental premises, namely 'that inscriptions are not just disembodied words that can be studied in isolation' (p. 2). In order to account for the materiality and visuality of the inscriptions, the individual chapters indeed contain numerous photographs and drawings and the arguments are supported by extensive visual analyses. It is regrettable then that the images are only in black and white and the overall quality is not as good as one would hope in a volume that addresses the visual qualities of inscriptions and the act of viewing. However, this problem is more indicative of the nature of academic publishing than of any shortcomings of the authors. My other quibble about this book is that there is no obvious structure or partition of the volume and it is left to the reader to identify the similarities and differences and the many shared themes in the use of writing by different cultures and across time. Antony Eastmond recognises this in his excellent afterword that comes to the rescue by synthesising the vastly different papers under headings such as multilingual inscriptions, the mediation of craftsmen, inscriptions and entrances, inscriptions and authority, pseudo-writing, inscriptions and identity and, lastly, the beauty of writing. One wonders whether these could have served as the guiding principles in the form of sub-sections throughout the book. Eastmond's fundamental ideas might have served the reader better as part of the introduction.

Overall, this book covers a broad and complex topic successfully. The eleven articles are thought-provoking and engaging despite their different scopes and level of in-depth discussions. Together they provide a comprehensive and very accessible overview of the production and use of inscriptions in the late antique and medieval world. As such the volume introduces the reader to the diverse functions, contexts, subject matters and visual strategies that characterise the use of writing as art. The disciplinary and chronological range enables cross-cultural dialogue and the diversity of methods and contexts will without doubt generate new approaches to the future study of inscriptions. This book is a representative and inspiring collection of original research on the material and visual aspects of writing as art in the widest possible sense and will prove useful for students and scholars alike.

NADINE SCHIBILLE CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE

IRAMAT-CEB


Jiawen Liu

Lilian Guillemeney

Arnaud Choux

Agnès Maitre

Benjamin Abécassis

Laurent Coolen
email: laurent.coolen@insp.jussieu.fr

Agnès Maître

Fourier-imaging of single self-assembled CdSe nanoplatelet chains and clusters

Keywords:

temperatures for stacked NPLs and was tentatively attributed to phonon coupling [START_REF] Tessier | Phonon line emission revealed by self-assembly of colloidal nanoplatelets[END_REF] , p-state emission [START_REF] Achtstein | p-state luminescence in CdSe nanoplatelets : role of lateral confinement and a longitudinal optical phonon bottleneck[END_REF] , delocalized excimer states [START_REF] Diroll | Semiconductor nanoplatelet excimers[END_REF] , surface states [START_REF] Yu | Effect of lateral size and surface passivation on the near-band-edge excitonic emission from quasi-two-dimensional CdSe nanoplatelets[END_REF] and most recently to negativelycharged trions [START_REF] Shornikova | Negatively charged excitons in CdSe nanoplatelets[END_REF] . Förster resonance energy transfer (FRET) has also been evidenced between stacked platelets 8,[START_REF] Guzelturk | Stacking in colloidal nanoplatelets : tuning excitonic properties[END_REF] with transfer rates [START_REF] Liu | Long range energy transfer in self-assembled stacks of semi-conducting nanoplatelets[END_REF] up to (1.5 ps) -1 . By a careful control of the ligands and solvents, NPLs can be assembled into linear chains of a few hundred nm to a few µm, with good photostability and brightness, excellent order and highly uniform inter-NPL distance [START_REF] Jana | CdSe nanoplatelets : living polymers[END_REF] . Ligand-induced strains within platelets can create a twist of these NPL chains [START_REF] Jana | Ligand induced twisting of nanoplatelets and their self-assembly into chiral ribbons[END_REF][START_REF] Kim | Stacking of colloidal CdSe nanoplatelets into twisted ribbon superstructures[END_REF] and may be responsible for the recently-observed permanent dipole parallel to the chain [START_REF] Dozov | Probing permanent dipoles in CdSe nanoplatelets using transient electric birefringence[END_REF] .

A key characteristic of a fluorescent system is the orientation of its radiating dipole, with implications for orientation and conformation tracking in bio-imaging [START_REF] Brokmann | Orientational imaging and tracking of single CdSe nanocrystals by defocused microscopy[END_REF] and superresolution [START_REF] Backlund | Simultaneous, accurate measurement of the 3D position and orientation of single molecules[END_REF] , for directional emission and light extraction in opto-electronics [START_REF] Kim | Pushing the efficiency envelope for semiconductor nanocrystal-based electroluminescence devices using anisotropic nanocrystals[END_REF] or for coupling and Purcell efficiency in nanophotonics and plasmonics [START_REF] Vion | Controlled modification of single colloidal CdSe/ZnS nanocrystal fluorescence through interactions with a gold surface[END_REF][START_REF] Jazi | Measuring the orientation of a single CdSe/CdS nanocrystal at the end of a near-field tip for the realization of a versatile active SNOM probe[END_REF] . A corollary question is how many dipoles contribute to the emission. For instance, because their emission originates from two degenerate states of orthogonal dipole orientations, CdSe NPLs can be well described by an incoherent sum of two in-plane dipoles [START_REF] Scott | Directed emission of CdSe nanoplatelets originating from strongly anisotropic 2D electronic structure[END_REF][START_REF] Ma | Anisotropic photoluminescence from isotropic optical transition dipoles in semiconductor nanoplatelets[END_REF][START_REF] Feng | Consequence of shape elongation on emission asymmetry for colloidal CdSe/CdS nanoplatelets[END_REF] . This can be an advantage, for instance, for light extraction in light-emitting diodes or for energy-funneling strategies in photovoltaics [START_REF] Scott | Directed emission of CdSe nanoplatelets originating from strongly anisotropic 2D electronic structure[END_REF] . Other two-dimensional systems have also been investigated [START_REF] Xiao | Dipole orientation shift of Ga 2Se2 by quantum confinement[END_REF] in order to demonstrate verticaldipole emission as it would provide enhanced coupling to plasmonic surfaces or photonic waveguides [START_REF] Brotons-Gisbert | Out-of-plane orientation of luminescent excitons in two-dimensional indium selenide[END_REF] or to Förster-transfer donors [START_REF] Erdem | Orientation-controlled nonradiative energy transfer to colloidal nanoplatelets : engineering dipole orientation factor[END_REF] . Vertical deposition of platelets by thick-shell growth [START_REF] Feng | Probing the fluorescence dipoles of single cubic CdSe/CdS nanoplatelets with vertical or horizontal orientations[END_REF] or by air-liquid interface self-assembly [START_REF] Gao | CdSe nanoplatelet films with controlled orientation of their transition dipole moment[END_REF][START_REF] Erdem | Orientation-controlled nonradiative energy transfer to colloidal nanoplatelets : engineering dipole orientation factor[END_REF] was also demonstrated.

By combined polarimetric and Fourier-image analyses, the different dipoles components of a single fluorescent nano-emitter can be discriminated [START_REF] Feng | Consequence of shape elongation on emission asymmetry for colloidal CdSe/CdS nanoplatelets[END_REF][START_REF] Feng | Probing the fluorescence dipoles of single cubic CdSe/CdS nanoplatelets with vertical or horizontal orientations[END_REF][START_REF] Lethiec | Measurement of three-dimensional dipole orientation of a single fluorescent nanoemitter by emission polarization analysis[END_REF] . In this paper, we analyse the in-plane and out-of-plane dipoles of single isolated platelets and of NPL stacks of various lengths. We show that, while no out-of-plane contribution can be resolved (< 0.03) for isolated NPLs, a clear out-of-plane dipole appears and grows as NPLs tend to cluster and assemble into longer chains. We discuss various hypotheses in relation with the NPL's tilt and deformations and the chain's internal electric dipole.

Results :

Figure 1(a) shows a transmission electron microscopy (TEM) image of the CdSe nanoplatelets, synthesized as described in ref. 24. They present a well-controlled rectangular shape with 20-nm length and 7-nm width (with respective 4-nm and 2-nm dispersions). Some overlapping between platelets (darker grey shade) indicates a spontaneous tendency to stack together. Figure 1(c) plots the NPL absorption and emission spectra. The very low 2-nm Stokes shift is characteristic of NPLs. The 549-nm emission wavelength is associated with a 1.5-nm thickness : 6 Cd layers and 5 Se layers. Analysis of single-NPL emission spectra has shown that the inhomogeneous broadening is negligible for these samples [START_REF] Liu | Long range energy transfer in self-assembled stacks of semi-conducting nanoplatelets[END_REF] . Given their extreme shape anisotropy, the NPLs' emission wavelength is solely dependent on their thickness, which is controlled during the synthesis with monolayer precision 2 .

Two different NPL chain samples were self-assembled as in ref. 24 (see Methods), one "long-chain" sample with length 1-2 µm (fig. 1(b)) and one "short-chain" sample with lengths 100-500 nm. The long chains present a twist which was discussed in ref. 26 and attributed to ligand-induced internal NPL strain. The NPL center-to-center distance can be estimated from high-resolution TEM images (see S.I. in ref. 24 for details) as 5.7 nm.

(c) Absorption (cuvette measurement) and emission (microphotoluminescence) spectra of isolated NPLs, emission spectrum of NPL chains (microphotoluminescence).

A CCD image of a single long chain under wide-field mercury-lamp illumination is shown on fig. 2(a). The sample consisted in a glass slide with emitters covered by a polymer (polymethylmetacrylate -PMMA), observed with a 1.4 numerical-aperture objective (fig. 2(b)). This configuration was chosen so that the radiation pattern was strongly dependent on the different emitting dipole contributions. For comparison, three different PMMA thicknesses were used : 130, 180 and 210 nm (measured with 5 nm precision by profilometry). We excited the chains at their centre and used Fourier-plane imaging (see Methods) to measure the radiation pattern of single NPL chains. Figure 2(c) shows the Fourier-plane images of three long chains under these different configurations. The radius corresponds to the maximal collected angle 𝜃𝜃 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = sin -1 �𝑁𝑁. 𝐴𝐴./𝑛𝑛 𝑔𝑔𝑐𝑐𝑔𝑔𝑔𝑔𝑔𝑔 � = 69°. The maximal emission is directed along the chain axis, in agreement with the expectation that the in-plane NPL dipoles (which are perpendicular to the chain axis : direction Φ on fig. 2(c)) radiate mainly into their orthogonal direction.

The measured radiation patterns for typical chains are plotted in fig. 2(d) along planes parallel and orthogonal to the chain axis. These patterns are very different depending on the PMMA thickness because the collected electric field is a sum of direct emission and emission reflected by the glass-air interface. However, some common features arise : a lobe at normal 0° angle ; a sharp change or peak at the critical angle 𝜃𝜃 𝑐𝑐 = sin -1 �1/𝑛𝑛 𝑔𝑔𝑐𝑐𝑔𝑔𝑔𝑔𝑔𝑔 � = 42° ; more or less strong lobes at 𝜃𝜃 > 𝜃𝜃 𝑐𝑐 corresponding to total internal reflection of the emission.

We fit the radiation patterns by an incoherent sum of three dipoles. For all samples considered in this paper, we will label ∥ ,1 the stronger NPL in-plane dipole, ∥ ,2 the weaker in-plane dipole, and ⊥ the out-of-plane dipole. Note that "in plane" will refer to the plane of the nanoplatelet. For a single NPL deposited horizontally on the substrate, in-plane dipoles ∥ ,1 and ∥ ,2 will be horizontal, while the out-of-plane direction ⊥ will be vertical. However for the NPL chain, dipole ⊥ is horizontal and parallel to the chain axis, while dipole ∥ ,1 is horizontal and orthogonal to the chain axis, and dipole ∥ ,2 is vertical (fig. 2(e)). We describe the weight of each contributing dipole by a coefficient 𝜂𝜂 proportional to the square of its dipole moment and normalized so that

𝜂𝜂 ∥,1 + 𝜂𝜂 ∥,2 + 𝜂𝜂 ⊥ = 1
The fitted radiation patterns (calculated following ref. 37) are plotted as solid lines on fig. 2(d). The overall agreement between experimental and fitted curves is excellent. We estimate (Fig. S1) the general precision of the fitted values to ± 0.03 for the out-of-plane coefficient 𝜂𝜂 ⊥ (which will be our main focus thereafter) and ± 0.05 for the weaker in-plane coefficient 𝜂𝜂 ∥,2 . Note that the angles 𝜃𝜃 ~ 0 are subject to very strong noise because they are inferred from just a few pixels on the Fourier image. Some deviation from the model is observed at higher ( 𝜃𝜃 > 60°) angles and may be caused by objective aberrations. Similar 𝜂𝜂 coefficients are obtained for all chains. The radiation patterns with the different PMMA thicknesses, although qualitatively very different, can all be fitted with very close 𝜂𝜂 values : this is a striking confirmation of the quality of our measurement of the three dipole contributions. Further support for our measurement is provided by comparison with polarization analysis. Figure 3(a) shows a typical emission polarimetric curve (obtained as described in ref. 35) from which an experimental degree of polarization 𝛿𝛿 𝑒𝑒𝑒𝑒𝑒𝑒 = (𝐼𝐼 𝑚𝑚𝑔𝑔𝑒𝑒 -𝐼𝐼 𝑚𝑚𝑚𝑚𝑚𝑚 ) (𝐼𝐼 𝑚𝑚𝑔𝑔𝑒𝑒 + 𝐼𝐼 𝑚𝑚𝑚𝑚𝑚𝑚 ) ⁄ = 0.30 can be fitted. Figure 3(b) shows the theoretical degree of polarization (calculation outlined in Methods) as a function of the dipole contributions 𝜂𝜂 ∥,2 and 𝜂𝜂 ⊥ (keeping in mind that 𝜂𝜂 ∥,1 + 𝜂𝜂 ∥,2 + 𝜂𝜂 ⊥ = 1). It can be noted that maximally-polarized emission is obtained when there is a single horizontal dipole (𝜂𝜂 ∥,1 = 1 or 𝜂𝜂 ⊥ = 1) while the emission is unpolarised when there is a single vertical dipole (𝜂𝜂 ∥,2 = 1) or when the two horizontal dipoles have the same moment ( 𝜂𝜂 ∥,1 = 𝜂𝜂 ⊥ ). For the parameters 𝜂𝜂 obtained from the Fourier image, the theoretical degree of polarization 𝛿𝛿 𝑡𝑡ℎ𝑒𝑒𝑐𝑐 = 0.30 is in perfect agreement with the measured degree of polarization 𝛿𝛿 𝑒𝑒𝑒𝑒𝑒𝑒 = 0.30. Figure 3(c) compares these values of 𝛿𝛿, experimental and theoretical (from 𝜂𝜂 factors), for all emitters considered in this paper. A remarkable agreement is always found between these two values, again validating the precision of our measured 𝜂𝜂 coefficients. We considered as a reference a solution of dispersed (non assembled) NPLs deposited on a glass slide. Such CdSe platelets are known to deposit horizontally on the substrate [START_REF] Feng | Consequence of shape elongation on emission asymmetry for colloidal CdSe/CdS nanoplatelets[END_REF] . For most emitters, the photon correlation function 𝑔𝑔 [START_REF] Ithurria | Colloidal nanoplatelets with two-dimensional electronic structure[END_REF] (𝜏𝜏) (fig. 4(a), dotted line) measured in Hanbury-Brown and Twiss configuration showed clear antibunching (single photon emission). The ratio, here labelled 𝑔𝑔 0 , between the area of the zero-delay peak and the average area of the other peaks, was in the range 0.06-0.40. This shows that multi-exciton radiative recombination is quenched by Auger effect, as 𝑔𝑔 0 is an estimate of the ratio between the biexciton and exciton quantum yield [START_REF] Nair | Biexciton quantum yield of single semiconductor nanocrystals from photon statistics[END_REF] . Given the area (around 140 nm²) of our platelets, this result is in agreement with ref. 39 : Ma et al. found 𝑔𝑔 0 close to 1 for NPLs larger than 150-200 nm² and decreased for smaller NPLs due to enhanced Auger interactions. For the emitter in fig. 4(a), we find 𝑔𝑔 0 = 0.14, indicating that we have a single platelet. The radiation pattern (fig. 4(b)) can be fitted by a sum of 2 horizontal (in-plane) dipoles, and the presence of a third vertical (out-of-plane) dipole can be excluded (see fig. S2(a) for precision analysis). Our measurement was further confirmed by comparing two measurement conditions, with or without a 30-nm PMMA film : we found 𝜂𝜂 ⊥ = 0 for the two configurations (fig. S2(b)).

Temporal post-selection can be used to remove the biexcitonic contribution (as explained in fig. S4). For some emitters however, we still find only incomplete antibunching (𝑔𝑔 0 > 0) (fig. 4(c)), and in some cases no antibunching (𝑔𝑔 0 ~ 1). We attribute these cases to clusters of platelets. It was seen already on fig. 1(a) that the isolated platelets tend to aggregate, parallel to each other (see also fig. S14). This is confirmed by decay and intensitytime trace curves (fig. S5) : a clear difference appears between the general emission properties of the single NPLs and the NPL cluster. The cluster radiation pattern in fig. 4(d) reveals two horizontal in-plane dipoles, showing that the clusters deposit horizontally like the single NPLs, but also a third vertical (out-of-plane) dipole which was not seen for the single NPLs. A similar out-of-plane component was found for all clusters. We also observed a few instances of vertical (on the edge) cluster deposition, with similar out-of-plane dipole : these cases are presented in section H of the Supporting material. Eventually, the measured dipoles coefficients 𝜂𝜂 are summarized in fig. 5 for single emitters of each type : long chains, shorter chains, clusters and single platelets. The main contributions are the two in-plane dipoles, parallel to the NPL plane, in agreement with our previous observations on various NPL geometries [START_REF] Feng | Consequence of shape elongation on emission asymmetry for colloidal CdSe/CdS nanoplatelets[END_REF][START_REF] Feng | Probing the fluorescence dipoles of single cubic CdSe/CdS nanoplatelets with vertical or horizontal orientations[END_REF] . The in-plane dipolar anisotropy ratio 𝜂𝜂 ∥,2 𝜂𝜂 ∥,1 ⁄ is 0.43 for the single NPLs, 0.59 for the clusters and 0.42 for the chains : it seems quite similar for the different types of emitters and related mostly to the NPL rectangular shape. It is probably caused by the dielectric shape of the rectangles, which enhance the dipole along the NPL elongation axis [START_REF] Ma | Anisotropic photoluminescence from isotropic optical transition dipoles in semiconductor nanoplatelets[END_REF][START_REF] Feng | Consequence of shape elongation on emission asymmetry for colloidal CdSe/CdS nanoplatelets[END_REF][START_REF] Rodina | Effect of dielectric confinement on optical properties of colloidal nanostructures[END_REF] . For the clusters, the distribution of 𝜂𝜂 ∥,2 𝜂𝜂 ∥,1 ⁄ values is broader, possibly because, for the clusters, the platelets do not stack in well aligned assemblies, as can be seen on fig. 1(a) where the different rectangles are not parallel (see also fig. S14). The obtained values are similar for the two chain samples, showing no influence of either the chain twist or its length over hundred-nm scales (TEM images show that the NPL rotation occurs in limited portions of the chains [START_REF] Jana | Ligand induced twisting of nanoplatelets and their self-assembly into chiral ribbons[END_REF] and most NPLs form straight stacks, so the twisted chains still have a similar ratio 𝜂𝜂 ∥,2 𝜂𝜂 ∥,1 ⁄

). The most striking difference between samples is that, while the NPL platelets show only in-plane dipoles (as was reported already by us [START_REF] Feng | Consequence of shape elongation on emission asymmetry for colloidal CdSe/CdS nanoplatelets[END_REF][START_REF] Feng | Probing the fluorescence dipoles of single cubic CdSe/CdS nanoplatelets with vertical or horizontal orientations[END_REF] as well as other authors [START_REF] Scott | Directed emission of CdSe nanoplatelets originating from strongly anisotropic 2D electronic structure[END_REF][START_REF] Ma | Anisotropic photoluminescence from isotropic optical transition dipoles in semiconductor nanoplatelets[END_REF] ), it is not the case for the NPL chains and clusters. Figure 6 plots the out-of-plane coefficient 𝜂𝜂 ⊥ as a function of the number 𝑁𝑁 of emitters in the assembly. This number is of the order of 35 for the 100-500 nm chains and 250 for the 1-2 µm chains (note that not all 250 NPLs are excited by the laser spot). For the clusters, it can be estimated from the antibunching curves by assuming that they are a sum of 𝑁𝑁 identical single-photon sources so that 𝑔𝑔 0 = 1 -1 𝑁𝑁 ⁄ . The clusters with higher 𝑔𝑔 0 correspond to a large 𝑁𝑁 with large uncertainty and can be distinguished from the smaller clusters for which 𝑔𝑔 0 is significantly lower than 1.

Finally, figure 6 shows a continuous increase of the out-of-plane dipole with the number of NPLs in the stack : from 𝜂𝜂 ~ 0 for the single platelets, to 0.05 for the small clusters (𝑁𝑁 ~ 2-5), to 0.1 for the larger clusters and 0.12 for the chains. We emphasize that it is the precision of our microphotoluminescence analysis protocol which allowed us to reveal this new dipole component, while it remained hidden in previous reports [START_REF] Gao | CdSe nanoplatelet films with controlled orientation of their transition dipole moment[END_REF][START_REF] Abécassis | Self-assembly of CdSe nanoplatelets into giant micrometer-scale needles emitting polarized light[END_REF] . The origin of this outof-plane component will be discussed below.

Figure 6 : out-of-plane dipole component for various emitters, either isolated emitters (measured in the two configurations : with or without PMMA film) or chains, plotted as a function of the number of platelets in this emitter (obtained from 𝑁𝑁 = 1/(1 -𝑔𝑔 0 ) for the isolated emitters -NPL or clustersand from their length for the chains).

Discussion :

A first hypothesis is that this dipole component originates from the elongated dielectric shape of the NPL chain out of a purely optical (nano-antenna) effect. Indeed for dipoles in an anisotropic dielectric structure the dipole component along the elongation axis is enhanced with respect to the other components [START_REF] Rodina | Effect of dielectric confinement on optical properties of colloidal nanostructures[END_REF] . This is probably the reason for the polarized emission of rectangular platelets [START_REF] Feng | Consequence of shape elongation on emission asymmetry for colloidal CdSe/CdS nanoplatelets[END_REF] . We performed finite difference time domain (FDTD) simulations of the NPL chain (see full discussion in S.I. section C) and found that the dipole along the chain axis was indeed enhanced as the number of NPL increased. This effects begins to appear for just a few platelets and saturates around 5-10 platelets (fig. S6(b)). This corresponds to a length of 30-60 nm, when the NPL chain begins to be longer along the chain axis than along the axes of the NPL plane. However, because the chain is a succession of very thin high-index platelets and no just a µm-length block of high index, the antenna effect along the chain axis is not very strong. The enhancement achieved is only by 26% for the out-of-plane dipole, relative to the other dipoles. In order for the chain's out-of-plane dipole 𝜂𝜂 ⊥ ~ 0.12 to be explained only by a dielectric optical effect, the out-of-plane dipole of a single platelet would have to be 𝜂𝜂 ⊥ ~ 0.08 (see section C in S.I.), which is clearly excluded by our measurements. The emission of in-plane dipoles, even modified by the dielectric chain of the NPL chain, cannot account alone for our measurements (fig. S6(d)). Even though the FDTD model might not give a fully accurate description of the experimental chain structure, the order of magnitude of the dielectric optical effect is far from sufficient to explain our observations.

Having excluded optical effects, we turn to the electron-hole wavefunction. We first note that the excitation power is sufficiently low to ensure that only one exciton is excited in the whole chain per laser pulse (see S.I. -section D). The degree of polarization remained the same for all excitation powers, as well as the decay curve, while the emitted intensity was a linear function of the exictation power (figs. S7, S8, S9). Exciton-exciton interactions can thus be ruled out. We have also measured the decay curves and emission spectra along the two polarizations parallel and perpendicular to the chain and found no difference (fig. S10). We thus have no sign to support that the emerging out-of-plane dipole originates from a novel transition state.

The vertical confinement is extremely large for nanoplatelets so that the electron-lighthole transition is much higher in energy than the electron-heavy-hole transition 2 . Electronheavy hole pairs can have ±1 or ±2 momentum [START_REF] Chuang | Physics of Optoelectronic devices[END_REF] . The room-temperature emission originates only from the degenerate ±1 transitions [START_REF] Biadala | Recombination dynamics of band edge excitons in quasi-two-dimensional CdSe nanoplatelets[END_REF] which is equivalent to an incoherent sum of two orthogonal in-plane dipoles. It is thus well understood why the electron-hole recombination in platelets shows no out-of-plane dipole. For nanocrystals, the exciton fine structure can theoretically present a third dipole component [START_REF] Efros | Band-edge exciton in quantum dots of semiconductors with a degenerate valence band: dark and bright exciton states[END_REF] but it is not the case for nanoplatelets.

Other emission mechanisms have been proposed in the literature, in particular in order to explain the second redshifted luminescence peak at low temperature [START_REF] Tessier | Phonon line emission revealed by self-assembly of colloidal nanoplatelets[END_REF] : phonon coupling [START_REF] Tessier | Phonon line emission revealed by self-assembly of colloidal nanoplatelets[END_REF] , p-state emission [START_REF] Achtstein | p-state luminescence in CdSe nanoplatelets : role of lateral confinement and a longitudinal optical phonon bottleneck[END_REF] , excimers [START_REF] Diroll | Semiconductor nanoplatelet excimers[END_REF] , surface states [START_REF] Yu | Effect of lateral size and surface passivation on the near-band-edge excitonic emission from quasi-two-dimensional CdSe nanoplatelets[END_REF] , energy splitting by different dielectric confinements [START_REF] Movilla | Dielectric confinement enables molecular coupling in stacked colloidal nanoplatelets[END_REF] and most recently trions [START_REF] Shornikova | Negatively charged excitons in CdSe nanoplatelets[END_REF] . Discussions of the different hypotheses and whether they are related to NPL stacking can be found in refs 20 and 22. In all experimental reports, this second peak contribution occurred only at low temperature (below 160 K) [START_REF] Yu | Effect of lateral size and surface passivation on the near-band-edge excitonic emission from quasi-two-dimensional CdSe nanoplatelets[END_REF] . We have also observed this second peak on NPL chains at low temperatures (fig. S11). It clearly disappeared above 200 K so that this second peak is not contributing to our room-temperature measurements. We mention also that we have recently analysed FRET exciton diffusion within NPL chains at room temperature [START_REF] Liu | Long range energy transfer in self-assembled stacks of semi-conducting nanoplatelets[END_REF] , but FRET is an incoherent nonradiative mechanism so that it should not modify the exciton wavefunction in a platelet.

It can also be noted that the platelets are not stacked exactly orthogonal to the chain axis : a slight tilt can be observed in the inset of fig. 1(b), so that a small component of the NPL dipole is in fact along the stacking axis. A statistical analysis of the TEM images shows that the NPL tilt angle is on average 7°, which, within a very simple geometric model, seems rather insufficient to induce the observed 0.12 out-of-plane dipole (see S.I. section G). However, a third dipole component may also appear if the NPL is not planar but slightly twisted. Such a twist would be difficult to observe on NPL-chain TEM images but has been demonstrated on single rectangular NPLs and is seen on NPL clusters (fig. S14). It is caused by the internal strain due to non-uniform ligand coverage [START_REF] Jana | Ligand induced twisting of nanoplatelets and their self-assembly into chiral ribbons[END_REF] . These strain and deformation are responsible for the helicoidal assembly of the NPL chains observed in fig. 1(b). Other authors have discussed the effect of NPL internal strain [START_REF] Llusar | Strain in lattice-mismatched CdSe-based core/shell nanoplatelets[END_REF] and ligand coverage [START_REF] Antanovich | Self-assembly of CdSe nanoplatelets into stacks of controlled size induced by ligand exchange[END_REF] on the emission wavelength. Recently, transient electric birefringence measurements [START_REF] Dozov | Probing permanent dipoles in CdSe nanoplatelets using transient electric birefringence[END_REF] on chains of 20 to 90 NPLs have demonstrated a permanent dipole along the chain axis, which was attributed to such straininduced shape deformation. It seems plausible that these deformations can also be responsible for our observed out-of-plane transition dipole. This explanation would be compatible with the observation that the out-of-plane dipole develops when the number of platelets increases up to around 5-10, but is similar for the 35-NPL and the 250-NPL chains : strain and deformations are not expected to lead to mechanical interactions between platelets over such large length scales (hundreds of nanometers).

Conclusion:

We have analysed the luminescence of single nanoplatelets, clusters and chains of nanoplatelets. We used Fourier imaging to measure the different radiation dipole components. By comparing the result with polarization measurements and by comparing different measurement conditions (PMMA thicknesses), we were able to estimate the uncertainty to only ± 0.03 and 0.05 respectively for the out-of-plane (normal to the NPL plane) and minor in-plane contributions. For single platelets, we found no out-of-plane dipoles, in agreement with previous reports and with theoretical considerations. For NPL clusters and chains, on the other hand, we measured a minor but significant out-of-plane dipole, which increased generally as a function of the number of platelets. We discussed various mechanisms for the presence of this dipole and suggest that it might be related to a straininduced NPL deformation within the NPL assembly, with an enhancement by a dielectric antenna effect. A better understanding of the role of self-assembly on the emission dipole could be obtained by further high-resolution electron imaging and a comparison with numerical models of the NPL crystalline structure and internal strain. Tuning the distance between neighbour platelets by changing the ligands would also provide a way to adjust the NPL mechanical interactions. We emphasize that it is our dipole analysis protocol, combining Fourier imaging and polarimetry, which allows to probe dipole components in different emitting systems with record precision thanks to the design of optimal experimental configuration (such as PMMA thickness). The method which is demonstrated here can have a wide range of applications in fundamental study of optical and electrical properties of semiconducting single emitters or two-dimensional materials, such as perovskite quantum dots and transition metal dichalcogenide semiconductors.

Methods :

Sample preparation :

Nanoplatelets synthesis: first we prepared cadmium oleate from a mixture of dissolved Sodium oleate and Cadmium nitrate tetrahydrate through a careful washing and drying process. Then we introduced cadmium oleate with commercial cadmium oleate and ODE in a three-neck flask equipped with a septum, a temperature controller and an air condenser. We carefully controlled the temperature and reaction ambience and added cadmium acetate dihydrate and oleic acid successively. After cooling the flask, we obtained a mixture containing 5-ML CdSe NPL, 3ML-CdSe NPL and quantum dots in solution, from which we separated 5-ML CdSe NPL by centrifugation.

Self-assembly of NPLs chains: an appropriate amount of 5ML-CdSe NPL solution was diluted in hexane and Oleic acid was then added, the amount of which is crutial to the length of assembled NPLs chains. The sample was sonicated for 10 minutes and the solvent was slowly evaporated. At this point we obtained highly-ordered NPLs chains.

More details about the synthesis and assembly protocol can be found in ref. 24.

Fluorescence microscopy : we performed optical measurements using a homebuilt inverted fluorescence microscope equipped with a laser scanning system. To image the NPLs chain, we used a mercury lamp to achieve a wide field excitation and used a CCD camera (QImaging Retiga EXi, pixel size 6.45 µm correspondin to 72nm on the image) for detection. A same objective (Olympus apochromat 100X 1.4N.A.), mounted on a piezo-electric stage, was used to focus the 470-nm diode laser beam (PDL 800-D PicoQuant, 70-ps pulses, 2.5-MHz rate) on the sample plane to scan/excite a single emitter and also to collect its emission. The scattered excitation light was filtered by a set of filters and only the 549 nm fluorescence light can reach the detectors.

During all measurements, the laser excitation power ranged typically from 5-to 7.5-nW (resp. 3-to 6-nW) for single NPLs (resp. assembled NPLs chains), within the linear excitation regime of the emitters.

To prepare the samples for optical study, the solution of single NPLs (respectively NPLs chains) was diluted 10000 times (resp. 500 times) in hexane and spin-coated on a glass slide at 4000 rpm for 40 s to get well-seperated single emitters. The deposited sample was then covered by a layer of PMMA with different thickness ranging from 130 to 210 nm as determined by profilometry. For theoretical calculations, the PMMA, glass and immersion oil will all be taken equal to 1.5.

Fourier plane imaging : to record the Fourier plane image, we used a Fourier lens to conjugate the rear focal plane (Fourier plane) of the objective to a EMCCD (Andor iXon Ultra 897) as described in details in ref. 35. The magnification of the conjugated image on the camera is 1.05X, with angular resolution ranging between 0.3° and 0.8° (corresponding to a collection angle from 0° to 69°).

Polarization measurement : we put a rotating half wave plate in front of a polarizing beam splitter cube (50:50), working equivalently to a rotating polarizer with angle denoted as α. The emission light from the microscope passed through this rotating system, was separated into reflection/transmision paths and detected by 2 avalanche photodiodes (PerkinElmer SPCM), respectively. We plot the normalized intensity on one photodiode as:

𝐼𝐼 𝑒𝑒𝑒𝑒𝑒𝑒 (𝛼𝛼) = 𝐼𝐼 1 𝐼𝐼 1 + 𝐼𝐼 2 in which 𝐼𝐼 1 and 𝐼𝐼 2 are the measured intensities on the two photodiodes. We use a 𝑐𝑐𝑐𝑐𝑐𝑐 [START_REF] Ithurria | Colloidal nanoplatelets with two-dimensional electronic structure[END_REF] configuration. We used the 470-nm pulsed laser (70ps pulse width) with 2.5MHz repitation rate to excite a single emitter and used the polarizing beam splitter cube (50:50) to separate the emitted photon flux into reflection/transmision paths to be detected by 2 avalanche photodiodes. The second-order cross correlation function 𝑔𝑔 [START_REF] Ithurria | Colloidal nanoplatelets with two-dimensional electronic structure[END_REF] (𝜏𝜏) is defined as 𝑔𝑔 [START_REF] Ithurria | Colloidal nanoplatelets with two-dimensional electronic structure[END_REF] (𝜏𝜏) = ⟨𝐼𝐼 1 (𝑡𝑡)𝐼𝐼 2 (𝑡𝑡 + 𝜏𝜏)⟩ ⟨𝐼𝐼 1 (𝑡𝑡)⟩⟨𝐼𝐼 2 (𝑡𝑡 + 𝜏𝜏)⟩ where 𝐼𝐼 1 (𝑡𝑡) and 𝐼𝐼 2 (𝑡𝑡) are the signal intensities on the two photodiodes and 𝜏𝜏 is the delay time.

Supporting information :

This material is available free of charge via the internet at http://pubs.acs.

Fig 1 :

 1 Fig 1 : TEM images of (a) single and clustered platelets and (b) 1-2 µm NPL chains. (c) Absorption (cuvette measurement) and emission (microphotoluminescence) spectra of isolated NPLs, emission spectrum of NPL chains (microphotoluminescence).

Figure 2 :

 2 Figure 2 : (a) CCD image of a long NPL chain under wide-field mercury lamp illumination. (b) Schematic of the measurement configuration. (c) Obtained Fourier images of typical single NPL chains for three

Figure 3 :

 3 Figure 3 : (a) Polarization analysis corresponding to the first chain in fig. 2(c). Blue dots: experimental data; red curve: cosine square function fitting. (b) Theoretical degree of polarization as a function of the components 𝜂𝜂 ∥,2 and 𝜂𝜂 ⊥ . (c) Relation between the experimental degree of polarization 𝛿𝛿 and its theoretical value (calculated with the 𝜂𝜂 coefficients from Fourier imaging) for isolated NPLs, clusters

Figure 4 :

 4 Figure 4 : Photon correlation function 𝑔𝑔 (2) (𝜏𝜏) for (a) a single NPL and (c) a cluster. Full lines : original data, dotted lines : after post-selection treatment. (b) and (d) : Corresponding radiation patterns (dots) and theoretical fits (lines).

Figure 5 :

 5 Figure 5 : Histogram of the measured coefficients 𝜂𝜂 ∥,1 (stronger in-plane dipole), 𝜂𝜂 ∥,2 (lower in-plane dipole) and 𝜂𝜂 ⊥ (out-of-plane dipole) for the different NPL samples : single NPLs, clusters, short chains and long chains. The average dipole contributions are given for each sample.

  Photon correlation function measurement:We measured the photon correlation function of isolated emitters under Hanbury-Brown and Twiss configuration. We used the 470-nm pulsed laser (70ps pulse width) with 2.5MHz repitation rate to excite a single emitter and used the polarizing beam splitter cube (50:50) to separate the emitted photon flux into reflection/transmision paths to be detected by 2 avalanche photodiodes. The second-order cross correlation function 𝑔𝑔[START_REF] Ithurria | Colloidal nanoplatelets with two-dimensional electronic structure[END_REF] (𝜏𝜏) is defined as

  org. A : Precision of 𝜂𝜂 coefficients. B : Identification of single NPLs. C : FTFT simulations. D : Excitation power dependence. E : Polarization effects. F : Temperature spectral dependence. G : Tilt of the NPL stacks. H : horizontal and vertical deposition of clusters.


M Froment
email: mfroment@lanl.gov

E Rougier

C Larmat

Z Lei

B Euser

S Kedar

J E Richardson

T Kawamura

P Lognonne

Lagrangian-based simulations of hypervelocity impact experiments on Mars regolith proxy

We conduct a parametric study of a novel Lagrangian numerical model of shock waves in granular media, with application to Mars regolith.

• We validate this model with a laboratory experiment in pumice sand with an impact velocity of 0.98 km/s.

• Amplitude of shock waves and transition to di↵erent regimes is explained by the model for the sensors placed vertically from the impact.

Introduction

InSight landed on Mars on November 26, 2018. Since then, the lander's robotic arm has placed a seismometer, the SEIS experiment, for the first time on the direct surface of the planet (Lognonne ´ et al., 2019). SEIS is a single seismic station completed by pres-sure and wind sensors [START_REF] Banfield | InSight Auxiliary Payload Sensor Suite (APSS)[END_REF]. The absence of other stations to form a network can make the assessment of source distance and azimuth sometimes challenging based on the first SEIS observations (Lognonne ´ et al., 2020;[START_REF] Giardini | The seismicity of Mars[END_REF]. Being able to identify signals produced by impacts would thus prove relevant to the mis-sion, as fresh craters can potentially be located by satellite imagery and provide a strong constraint on the source position [START_REF] Daubar | Impact-seismic investigations of the InSight mission[END_REF]. Current estimations and mea-sures of impact rates on Mars show a higher frequency of craters smaller than 10m di-ameter, with 10 times more craters in the range of [3.9, 5.5] m diameter created every lin et al., 2006). The expected rate of detection is estimated to about 8 impacts per year for the SEIS VBB [START_REF] Banerdt | Initial results from the InSight mission on Mars[END_REF], close to the pre-launch proposed rate (Lognonne ´ & Johnson, 2007;[START_REF] Daubar | Impact-seismic investigations of the InSight mission[END_REF]. The generation of seismic signals by such small events is dominated by the response of Mars regolith, a layer of unconsolidated rocky material covering the bedrock, which is supposedly desiccated at the InSight landing site close to Mars equator [START_REF] Morgan | A pre-landing assessment of regolith properties at the InSight landing site[END_REF]. First analyses have confirmed low seismic velocities, which might even be as low as 120 m/s for P waves at 0.5 m depth (Lognonne ´ et al., 2020). Physic-based shock propagation codes allow high-fidelity modeling of the shock waves generated by meteorite impacts, which transition to seismic waves at further distances and thus control the shape and amplitude of the seismic signal that could be recorded by SEIS. Such modeling requires the codes to be able to track discontinuous features in time and space, like material fractures and phase transitions caused by the shock. Moreover, small impacts are expected to happen mostly in a solid regime of high viscosity, making the capture of non-isotropic processes an important requirement for simulation softwares.

Another challenge of modeling impacts in Mars regolith is its granular nature: friction and grain displacement processes in the material are important and grain interaction can lead to non-linear behaviors that manifest as "force-chains" [START_REF] Sun | Some open problems in granular matter mechanics[END_REF][START_REF] Gao | From stress chains to acoustic emission[END_REF] and "fairy-castle" structures [START_REF] Hapke | Photometric studies of complex surfaces, with applications to the moon[END_REF][START_REF] Carrier | Physical properties of the lunar surface[END_REF] depending on the confining stress on the grains. Moreover, the material is porous, which leads to an enhanced attenuation of shocks compared to bulk materials [START_REF] Collins | Planetary impact processes in porous materials[END_REF]. Only now numerical methods to model impacts are starting to implement realistic, geologic materials as their target [START_REF] Güldemeister | Quantitative analysis of impactinduced seismic signals by numerical modeling[END_REF][START_REF] Pierazzo | Validation of numerical codes for impact and explosion cratering: Impacts on strengthless and metal targets[END_REF][START_REF] Wünnemann | A strain-based porosity model for use in hydrocode simulations of impacts and implications for transient crater growth in porous targets[END_REF]. Here, we use the novel Lagrangian mechanical software HOSS, based on a finite-discrete element formulation [START_REF] Munjiza | The combined finite-discrete element method[END_REF][START_REF] Munjiza | The combined finite-discrete element method[END_REF][START_REF] Munjiza | Large Strain Finite Element Method: A Practical Course[END_REF][START_REF] Munjiza | HOSS: An integrated platform for discontinua simulations[END_REF][START_REF] Lei | A framework for grand scale parallelization of the combined finite discrete element method in 2d[END_REF], to create a new numerical model of impacts in regolith. The lagrangian framework is appropriately tackling all modeling challenges stated above, as it allows for a straightforward description of discontinuities in unconsolidated materials and deviatoric stresses. Consequently, a better description of shear waves and surface processes is possible as well as non-isotropic impact processes.

In the following, we present the laboratory experiments we use to validate the numerical model, as well as the numerical method and the material model used to describe Mars regolith. We present results of a parametric study of the model where we identify which parameters control the transition to the di↵erent regimes of impacts, meaning from shock to plastic to elastic response of the material. We then present a comparison of the model predictions to the laboratory data, before finishing with discussions and conclusions.

2 Laboratory experiments and model.

Experiments

The validation of the novel numerical model presented in this paper is done with data from a series of laboratory impact experiments conducted at the NASA/AVGR facility [START_REF] Richardson | An experimental investigation of the seismic signal produced by hypervelocity impacts[END_REF]. The experimental setup is composed of a cylindrical tank, 1 meter in radius and in height, filled with a target bed and placed inside a chamber with a controlled atmosphere. Tests were monitored by 15 accelerometers buried into the target at di↵erent positions. Sampling rate is 10 5 s.

We focus on two experiments performed in an Earth atmosphere at Martian pressure of 5 to 10 torr, and on a target bed of pumice sand. This sand has a grain size of 0.1 to 0.2 mm, a porosity of 62%, and a composition and density similar to the Johnson Space Center (JSC) Mars-1 Regolith Simulant [START_REF] Allen | JSC Mars-1-Martian regolith simulant[END_REF]. In this study, the impactor is a 6.3 mm diameter bead with a mass of 0.29g made of Pyrex, and an impact velocity of 0.98 km/s.

Numerical model

The numerical model is based on a finite-discrete element representation (FDEM) used to handle the unconsolidated nature of Mars regolith. FDEM merges continuum solutions for the calculation of stresses as a function of deformation with the discrete element method for the resolution of fracture, fragmentation and contact interaction [START_REF] Munjiza | The combined finite-discrete element method[END_REF][START_REF] Munjiza | The combined finite-discrete element method[END_REF][START_REF] Munjiza | Large Strain Finite Element Method: A Practical Course[END_REF][START_REF] Munjiza | HOSS: An integrated platform for discontinua simulations[END_REF][START_REF] Lei | A framework for grand scale parallelization of the combined finite discrete element method in 2d[END_REF][START_REF] Lei | A generalized anisotropic deformation formulation for geomaterials[END_REF][START_REF] Lei | A non-locking composite tetrahedron element for the combined finite discrete element method[END_REF].

We generate meshes of tetrahedral elements covering a 30 sector of the experiment tank. The numerical volume is 90cm deep and wide and contains around 1,000,000 elements. Each Lagrangian finite element (FE) contains from approximatively 1000 grains of sand for the smallest ones close to the impactor (tetrahedrons of 1mm edges) and 1,000,000 grains of sand for the largest ones (tetrahedrons of 1cm edges), allowing for a mesoscale representation of the sand properties.

To simulate the grain displacements involved in impacts in unconsolidated material, HOSS treats the tetrahedral FEs as an unconsolidated heap where the elements in- pressure increasing linearly with strain, given a bulk modulus K el , as P (") = K el ". After a limit pressure P el is reached, the porous material undergoes grain displacement and grain crushing. This domain starts with a break of slope from K el to K trans and is followed by an exponential increase of pressure with deformation. The equation of this curve is :

P (") = P el + K trans m • ln(10) (10 m(" " el ) 1) for " " el . ( 1
)
where " is the strain, " el is the upper strain limit of the elastic regime and m is a parameter describing the exponent of the curve. K trans drives the slope of the pore-crush curve at the beginning of the crushing processes. Given two values of K trans , a lower value means that the material is easier to crush, because a lower amount of pressure is sucient to obtain the same amount of deformation as with a higher value. m is the expo-nent of the pore-crush curve and the same reasoning applies, i.e., a low m results in an easily crushable material.

Finally, when the material is fully crushed and all the porosity ↵ of the material disappears, the exponential curve morphs into a straight line with bulk modulus K fc of a non-porous rock of the same composition.

The SE (Figure 1, right) sets the limit deviatoric stress (i.e., yield stress) that can be sustained by the material for any given mean stress. In this simplified model, the yield curve first increases linearly with mean stress and upon reaching the yield limit (P Smax , S max ), it becomes constant, transitioning to a more viscous behavior. In the case of a granular material like sand, the cohesion S c of the material is zero.

The response of the impactor's material is represented using the Munjiza's elastic model [START_REF] Munjiza | Large Strain Finite Element Method: A Practical Course[END_REF][START_REF] Lei | A non-locking composite tetrahedron element for the combined finite discrete element method[END_REF]. The FE size and impact speed result in an integration time step of a few nanoseconds. Given the time scale of the experimental signals, the simulation need to be run up to a few milliseconds.

Results

Parametric study

This work focuses on the parameters K el , K trans , m, P el and P Smax . For each of these parameters, between 3 and 4 simulations are run to explore the e↵ect of their change on the shock wave properties. This first set of analysis is conducted without including Earth gravity to the simulation. The e↵ects of this additional force are discussed in section 3.2.

Literature on sand mechanical properties provide ranges of values for some of these parameters. The parameter m thus seems to be between 3 and 6 for the sand studied in [START_REF] Luo | E↵ect of mass density on the compressive behavior of dry sand under confinement at high strain rates[END_REF][START_REF] Yamamuro | One-dimensional compression of sands at high pressures[END_REF][START_REF] Yamamuro | E↵ect of strain rate on the stress-strain behavior of sand[END_REF]. The elastic p-wave velocities measured on Mars regolith simulants [START_REF] Morgan | A pre-landing assessment of regolith properties at the InSight landing site[END_REF] range between 80 m/s and 250 m/s and the Poisson's ratio is around 0.2, leading to K el roughly between 5MPa and 60MPa for a bulk density of 880 kg/m 3 . In many experiments [START_REF] Berney | Mechanical and Physical Properties of ASTM C33 Sand[END_REF][START_REF] Hyodo | Undrained monotonic and cyclic shear behaviour of sand under low and high confining stresses[END_REF], the shear response of sands tends to remain in the domain of Coulomb friction even above a few MPa of pressure, leading to P Smax > 10 6 Pa. ulus G, the velocity of a purely acoustic wave is v accoustic = In a first test, P Smax has been varied between 10 6 Pa down to 10 3 Pa. For P Smax > 10 5 Pa, the seismic waves show no visible change of amplitude, shape or velocity away from the impactor. Indeed, the stress values reached with these low-energy impacts are typically around 10 4 Pa. Only a few elements within 5cm of the impact undergo pressures higher than 10 6 Pa. Therefore, the yield strength has to be lowered to very low values of 10 4 or 10 3 Pa to produce a visible e↵ect on the shock wave away from the source.

These values are far from typical values of yield strength measured for sand [START_REF] Berney | Mechanical and Physical Properties of ASTM C33 Sand[END_REF] and can be considered unphysical, therefore the plastic wave is essentially una↵ected by realistic yield strengths.

Consequently, we focus on the transition between elastic and plastic domain. It is known in shock physics that a deflection in the Shock-Hugoniot curve at the onset of plasticity results in the generation of two waves: the elastic precursor, which travels at elastic speed in the medium, and a plastic wave with slower propagation velocity and higher attenuation. These features are generated by the elastic-plastic transition in the EOS model, if K trans < K el . This change of regime is evident on Figure 2 as a change of the slope of the evolution of the maximum pressure with distance. The break corresponds to the distance at which the maximum pressure falls below P el . Modeled signals for which the pressure exceeds P el show an elastic precursor followed by a plastic wave, but contain only an elastic wave in the other case.

Table 1 gathers a series of measures on the e↵ect of K el and K trans on the impact shock wave. Four experiments were ran with K el = G = 10 MPa and K trans varying between ⇠ 1 and ⇠ 8 MPa. The velocity of the generated elastic wave was measured by picking the acceleration arrival times. As K el > K trans , a plastic wave is also created, whose move-out velocity can be computed using the peak time of the pressure wave between sensors placed every 1cm. For our value of bulk mo r dulus K el and shear mod- To further analyse the e↵ect of the pore-crush regime, the exponent m of the porecrush curve is varied between 3 and 6, while the parameter K trans is fixed to a value of 1.5 MPa, and we repeat the same measurement as before. In Table 1, our results show that, at the scale of these experiments, m has only a moderate influence on the plastic wave velocity, as well as on the amplitude of the generated wave.

K el ⇢ = 107 m/s,

Volumetric Response of Pumice Sand

From the parametric study reported previously, it is possible to infer appropriate parameters to fit the experimental signals. To match the wave velocity measured on the vertical accelerometers of the AVGR shot, K el is set to 10 MPa. The elastic precursor being visible up to 42cm below the impact point in the experiments, P el must be lower than the maximum pressure reached at this point, which leads to P el = 1kPa. To match the amplitudes of the wave on each of the sensors, K trans is set to 6 MPa. The experimental data could not provide enough constraints on m or the parameters from the SE.

We thus set the exponent m to 5, a number found in some high-pressure experiments in several types of sands [START_REF] Yamamuro | One-dimensional compression of sands at high pressures[END_REF][START_REF] Yamamuro | E↵ect of strain rate on the stress-strain behavior of sand[END_REF][START_REF] Luo | E↵ect of mass density on the compressive behavior of dry sand under confinement at high strain rates[END_REF]. The SE yield point is set to a value of 1 MPa, too high to create any visible yield in our sand, and the friction coe cient is kept at 0.75. To study the e↵ects of gravity on the results, we include an initial acceleration of -9.81 m/s 2 to one simulation, letting the sand relax to an equilibrium over a few 100ms before the impact. Another simulation is run without gravity, but both use the same material model parameters as listed above. The resulting numerical and experimental waveforms are compared 21cm directly below the impact point on Figure 3 and 30cm horizontally from the impact point on Figure 4, both with and without the gravitational constraint.

On Figures 3 and4, the modeled acceleration wave has an amplitude 40% lower and 33% higher than the experimental signal for the vertical sensor with and without gravity, respectively; and up to 100% higher for the horizontal sensor with no gravity.

The velocity wave, however, ranges closer to the experimental signal. The arrival times at the vertical sensors match each other, in accordance with a measured vertical moveout velocity of 150 m/s. For the shallow sensors, we measure a horizontal move-out velocity closer to 80 m/s, while the modeled waves keep the same move-out velocity as for the vertical sensors, thus being ahead of time.

4 Discussion, Conclusions and Future Work

The presence of gravity improves significantly the modeled material response to the main shock. In the model without gravity, this response is weak enough so that the velocity of the vertical sensor remains negative after 5ms (Figure 3). On the shallow sen- sor, the modeled velocity reaches a constant positive value after 4ms when the acceleration vanishes (Figure 4). This indicates that the element attached to this sensor is in a non-accelerated motion, a "free-flight". The modeled signal with Earth gravity di↵er greatly. On Figure 3, we can see that the counter-response of the material to the impact is now strong enough to create a positive velocity on the vertical sensor, reproducing the behavior of pumice sand of the experiment. Acceleration on the shallow sensor displayed on Figure 4 doesn't show any longer evidence of free-flight but starts a cycle of falling down and rebounding as seen on the experimental data.

The parametric study suggests that the plastic yield, P Smax , has little influence on the shock wave. This is due to the fact that the stress level in our modeling reaches at most the order of 10 kPa, way lower than any documented plastic yield. The modeled material thus remains in a regime where the SE can be approximated by a simple Mohr-Coulomb surface. On the contrary, some questions remain on the e↵ect of the elastic shear modulus G of the material. In this study, G, which a↵ects both the shear wave and Rayleigh wave speed of an elastic material, was fixed once it became clear that the main shock is mostly driven by the EOS parameters, but shear-or Rayleigh waves might still be an explanation for the late-time discrepancies between the modeled and experimental waves that are not caused by gravity. Moreover, this study shows that the wave move-out velocity is not completely determined by the elastic bulk modulus K el , but rather lies between the expected speed of sound in a fluid v accoustic and the P-wave velocity in a solid v solid . A more thorough study of the influence of G could shed some light on the elastic speed of waves in granular media, which can neither be considered as a fluid nor as a traditional elastic solid, and will help calibrating the model with respect to the experiments.

The study of the pore-crush curve suggests that plastic processes in sand, such as pore collapse and grain displacement are particularly e cient in the shock attenuation, and that the slope of the pore-crush curve of the EOS is key in capturing this attenuation. Still, trade-o↵s exist between the model parameters analyzed. For example, parameters K trans and m, that define the pore-crush curve, play a role in the amplitude and peak time of the plastic wave. An increase in m could thus compensate for a decrease in K trans .The low pressure part of the curve is easier to constrain with the available data, but the scale of the experiments does not allow for a proper determination of the highpressure response. The high-pressure EOS and SE will be of higher importance in the case of real planetary impacts, where the energy involved is several orders of magnitude higher. For example, the impact velocity distributions computed for Mars from observed asteroid populations yield a mean impact velocity of 9.6 km/s [START_REF] Ivanov | Mars/Moon cratering rate ratio estimates[END_REF]. For better model accuracy at high pressures, other types of high-stress laboratory data or theoretical models should be considered in the future.

In conclusion, the final model captures the vertical wave's shape and amplitude for an impact velocity of 0.98 km/s. This proves that HOSS can reproduce the main characteristics of an impact shock wave in granular media. The results have shown to be more sensitive to variations on the EOS parameters than to variation on the SE parameters.

Gravity has proved to be a key parameter in the later stages of wave simulation by providing a more realistic material response. However, the arrival times and amplitudes recorded at the shallow sensors cannot be reproduced by this model. Understanding this discrepancy requires further study, as a non-spherical wavefront needs to be modeled. Future works will investigate the e↵ect of shear waves on the signal and the hypothesis of depthdependant elastic properties created by the constraint of sand by gravity, as it has al-ready been reported in literature [START_REF] Morgan | A pre-landing assessment of regolith properties at the InSight landing site[END_REF][START_REF] Van Den Wildenberg | Shock waves in weakly compressed granular media[END_REF].

This non linear constraint creates a dependance of the bulk modulus with pressure in the elastic domain. Improving the fidelity of HOSS' model to the experimental truth will bring more insight into the physics of shocks in granular, highly porous media and a new definition of equivalent seismic sources for impacts. Such new validated modeling capability will help predict the signal of small planetary impacts, for which surface porous regolith endures most of the shock. These small impact might be recorded by InSight, if close enough, and provide new information on the crustal seismic properties of Mars.

Figure 1 .

 1 Figure 1. Simplified representation of the Equation of State (left) and the Strength Equation (right) and their key parameters.

  teract only through frictional contact, with a Coulomb coe cient of friction of 0.75 for this study. Inside each FE, the material model is governed by two equations, depicted in Figure 1. One describes the volumetric response, or Equation of State (EOS), and the other the deviatoric response, or Strength Equation (SE). The EOS is a function of pressure with volumetric strain and has three di↵erent domains. The first one is elastic, with

Figure 2 .

 2 Figure 2. Evidence of an elastic and plastic regimes. (a) Shows the maximum modeled pressure recorded with distance for three di↵erent values of P el . In inset, a snapshot of a HOSS simulation of the 0.98 km/s shot, showing the amplitude of the velocity and the ejected sand elements 2.5ms after the impact. (b) Waveform in an area where P exceeds P el = 10 4 Pa. The dashed circle indicates the elastic precursor followed by the plastic wave. (c) Waveform in an area further away from the impact with only an elastic wave. P el appears to be an important parameter controlling the transition between these two regimes.

Figure 3 .

 3 Figure 3. Compared numerical and experimental vertical acceleration (left) and velocity (right) signals for the 0.98 km/s impact velocity shot, recorded at a sensor 21cm directly below the impact point. The solid blue line and the dashed light-blue line correspond to simulations performed with and without earth gravity, respectively. The simulation better matches the experiment when gravity is considered.

Figure 4 .

 4 Figure 4. Compared numerical and experimental vertical (a) and radial (b) signals for the 0.98 km/s impact velocity shot. Both accelerations and velocities are shown for the sensor 30 cm radially away from the impact point. The solid blue line and the dashed light-blue line correspond to simulations performed with and without earth gravity, respectively. Note that modeled signals have been shifted in time to obtain a better match (see text for details).

Table 1 .

 1 Parametric study of Ktrans (Runs 1 to 4) and m (Runs 5 to 8). Plastic wave velocities have been measured by recording the time at which pressure peaks as a function of range.Elastic wave velocities have been measured by picking the acceleration wave arrival time with a threshold as a function of range. The theoretical value for this elastic wave velocity is between 107 and 162 m/s, as explained below. Peak pressure is also given at 20cm.

	and

ilar value for each experiment, suggesting a good agreement with a rough linear Hugoniot model of P ⇠ V impact p K⇢.

Acknowledgments

This work is InSight contribution number 119 and LA-UR-19-32642. We thank the LANL-HPC environment for providing and maintaining the Los Alamos High-Performance Computing facilities and the NASA/AVGR facility for conducting the impact experiments.

We also thank the reviewers whose comments helped improve and clarify this manuscript.

Experimental data are in the process of being transferred to an online repository. More details on the parametric study can be found in the Master thesis of the author (Froment, 2020). This work is funded by the LANL Center for Space and Earth Science (CSES) project XWPB00 and the ARPE student program of the École Normale Supérieure Paris-Saclay. The French co-authors are acknowledging the support of CNES and ANR (under contract MAGIS ANR-19-CE31-0008-08).