Jean-Yves Blaise

Iwona Dudek

Exploring visually the known and the ill-known about Kraków's centre urban evolution: an information visualisation perspective

Keywords: Information visualisation, Temporal data, Uncertainty, Inferences, Reasoning, Heterogeneous data sets

Studying and depicting the design and transformations of urban structures have been a concern ever since the 19th century, both from the point of view of historians, and from the point of view of urban planners. Where exactly is the impact of « digital humanities » on the way we today can renew our means of investigation? How can we usefully support the analyst's reasoning tasks, by visual means, in the context of historical research, and at the scale of a city? This chapter introduces on real-case experiments carried out on the city centre of Kraków, former capital of Poland. Through these experiments we illustrate the fundamental issue of imperfect knowledge in historical sciences, the need and constraints of handling ill-defined temporal data, and the necessity to, at least, complement "classic" virtual reconstruction efforts with visual solutions that better match the nature of the underlying data -doubts -and the nature of a city -an heterogeneous collection of structures that differ not only in terms of morphology and use, but also in terms of documentation quality. We introduce an approach that bases on the idea that the gap between historical sciences one on hand, and information visualisation (InfoVis) on the other hand, should and can now be filled. Our record of experience shows the potential added-value of InfoVis-inspired abstract graphics in supporting reasoning tasks on the evolution of urban structures. Our contribution will illustrate on real cases in what the above mentioned methodological bridge can be a solution-provider in the context of urban analyses, and point out the actual scientific and technological locks we are facing.

Introduction

Studying and depicting the design and transformations of urban structures have been a concern ever since the 19th century, both from the point of view of historians, and from the point of view of urban planners. Where exactly is the impact of "digital humanities", or more precisely of digital technologies, on the way we today renew our means of investigation? How can we usefully support the analyst's reasoning tasks, by visual means, in the context of historical research, and at the scale of a city? What specific methodological bottlenecks does this context introduce? What can be done when there is simply not enough data to carry out a reconstruction, or when there is a need to formalise hypotheses that will back up a reconstruction process? How can we support reasoning tasks when our concern is not on a spatial pattern but a temporal pattern?

A prominent difficulty when wanting to analyse the evolution of a "city" in the broad sense is naturally the fact that the information available is sometimes scarce, or questionable, when not simply absent. Hence this chapter raises a still-open research question: how can analysts formalise the ill-known, and introduce it from a pragmatic point of view into contemporary information systems? But another difficulty is the heterogeneity of the objects under scrutiny. Consequently this chapter also underlines a key aspect of reasoning on a city, the step from analysing a single edifice to analysing an urban structure is not quantitative, it is primarily methodological. An urban structure is a system where interrelations, interdependencies, play a major role, may they be between edifices, between edifices and open spaces, or may they be between the urban fabric and a context -wars, floods, laws, aesthetics of a time, etc. In that sense, switching to the analysis of a whole urban structure may reveal interrelations, patterns of change, possible causal chains, and ultimately allow for information and knowledge discovery. This chapter however is not a theoretical discussion on "reconstructing the past of cities". It introduces real-case experiments carried out on the city centre of Kraków, former capital of Poland, and uses them as illustrations of some of the key scientific and technological locks we are facing when wanting to better understand, and better have others understand the way a city changed over time. Through these experiments we illustrate the fundamental issue of imperfect knowledge in historical sciences, the need and constraints of handling ill-defined temporal data, and the necessity to, at least, complement "classic" virtual reconstruction efforts with visual solutions that better match the nature of the underlying data -doubts -and the nature of a city -an heterogeneous collection of structures that differ not only in terms of morphology and use, but also in terms of documentation quality.

The city of Kraków developed significantly during the first six centuries of the second millennium, before entering a period of relative decline when the Swedish monarchs moved the capital of the kingdom to Warsaw. This relative decline constitutes an opportunity for us today, as the city experienced little significant change during the nineteenth and twentieth centuries compared to other cities of similar size. Moreover, years of preservation and investigative actions have resulted in the production of a large quantity of documents (descriptions, analyses, drawings, photographs, plans, etc.) which need to be collected, organised and visualised. Our research focuses on understanding, documenting, visualising the evolution of architectural and urban components (341 objects, 885 phases studied). Its inputs are primarily historical sources concerning directly these components, but also elements of context that can help spotting potential causal chains (legal issues, natural phenomena, fire propagation patterns, demography, wars and rulers, etc.).

We have been studying the evolution of Kraków's historic centre, at various scales, for over fifteen years now. We have consequently quite soon switched from analysing an edifice to analysing an urban area. This switch clearly introduced a methodological break, not only in numbers (more elements) but also and above all in terms of heterogeneity (different objects of study, as well as different quantity and/or quality of data, or different levels of knowledge). A common sense assertion would be to consider that as time passed by we got to know more and more about the changes that occurred in the city. And indeed we did uncover a number of facts about individual edifices, the urban layout, uses and practices of urban spaces, the defensive system, etc. But, to be true, as it is often the case in historical research, as time went by we also unveiled more and more open questions, more and more ill-knowns or unknowns. The reality of historical research on a large, heterogeneous corpus -i.e. a whole city -is sometimes such that the more one digs into the data, the more unknowns are revealed. To make it short, our experience underlines a sort-of counter-intuitive pattern: the proportion of unknowns or illknows grows with the time spent on a comprehensive analysis of a city's evolution.

But is that pattern really surprising? With time, we analyse more and more individual components of the city. But we also pull in more and more sources, more and more elements of context. Accordingly, we do not only add up the unknowns corresponding to each component, each piece of information, we also multiply doubts that arise over potential relations between components, components and context. A classic example of that trend is the fire propagation patterns in a city. If a source tells us a fire probably damaged an artefact A, there are chances it also had an impact on any B neighbour of A. And so not only is the information concerning A doubtful, but a whole chain of potential (and questionable) consequences is de facto created.

Furthermore, understanding a city's changes over time cannot be supported by only one or several "pictures" of its spatial layout at time t1, t2, …, tn (synchronic analysis). It also implies understanding temporal patterns that characterise these changes: rhythms, order, cycles, etc.

Hence the necessity for us to complement "assertive" visual results such as 3D models, with other analysis platforms, better suited to the handling of massive data sets, doubtful information, and temporal data. On what methodological and/or technological basis can such platforms be designed and built? As will be shown, reasoning visually on large information spaces is at the heart of a sub-field of information sciences, namely InfoVis (Information Visualisation) and its sister field visual analytics. Our intent in this chapter is to try and show through real cases that historical research about the past of cities can benefit from complementing photorealistic representations with abstract graphics inspired by the InfoVis paradigms and practices.

In a brief first section we give an overview of some of the mainstream practices in terms of virtual reconstructions of cities. We then discuss four major scientific challenges such initiatives raise: dealing with the ill-known, representing temporal data, ensuring the reproducibility of experiments, enabling the analysis of collections as such.

Finally, we briefly position InfoVis with regards to its legacies and to the general context of information technologies, and detail some of our key experiments. As will be shown, these graphics are aimed at helping the analyst to re-read the data available, filter and re-organise it, and ultimately to explore visually the known and the ill-known about Kraków's centre urban evolution.

Virtual reconstructions: practices and open methodological issues

With the raise of digital technologies over the past twenty years, a number of new tools (in the broad sense) have been introduced in the process of historical research and in its communication: digitisation platforms, online databases, information systems, virtual reconstructions, augmented reality disposals, immersive 3D platforms, and others. Giving a general overview of all these "new" opportunities is beyond the scope of this chapter: what we shall do here is mention three significant trends, birthed in the early 1990s, so as to pinpoint underlying methodological issues that we consider common, and still open.

Back in 1993 Patricia Alkhoven published a research that remains in many ways a landmark: "The changing image of the city" [START_REF] Alkhoven | The Changing Image of the City. A study of the transformation of the townscape using Computer-Aided Design[END_REF]. The author intermingles historical research on the evolution of the city of Heusden (Netherlands), with an architectural analysis of morphotypes, and with a significant 3D modelling effort that results in a series of "virtual reconstructions". The technology of the time is naturally today obsolete, but her research already exemplified pitfalls, work processes, potential benefits of using 3D models in the course of such a research: heterogeneous and untrustworthy inputs, pieces of general knowledge called in to counterbalance missing data, case by case inferences, power of seduction of virtual environments, etc. Today, building "virtual reconstructions" at the scale of a city has become a popular research goal. However there are nuances in the way that activity is conducted.

The initial virtual reconstruction paradigm can be described as an effort to translate the expert's understanding of a city's layout and components at time t into a set of geometric shapes distributed in space. The underlying geometric canvas can be obtained by various means, from old maps to contemporary digitisation campaigns. Alkhoven's 3D models partially base on a 1649 map by Joan Blaeu. The Virtual Leodium project [START_REF] Pfeiffer | Virtual Leodium: from AN Historical 3d City Scale Model to AN Archaeological Information System[END_REF] bases on a 3D survey of a physical model representing the city of Liège (Belgium) towards 1730. The Virtual Kyoto city model [START_REF] Takase | Virtual Kyoto: Visualization of historical city with 4D-GIS, virtual reality and web technologies[END_REF] integrates automatic generation of 3D city model using LIDAR data, 2D digital map and aerial photography. Significant research efforts are put today on trying to produce photo-realistic city models and publish them on the internet, with quite often more focus put on the technological suite than on the scientific added value.

But, as exemplified by Alkhoven's, the objective is not necessarily to reach to a photo-realistic anamorphosis, in the virtual world. It can be testing different geometric combinations, or fostering an educated debate among scientists. Non-photorealism (NPR) appears here as a potential alternative approach (e,g. [START_REF] Döllner | Non-Photorealism in 3D Geovirtual Environments[END_REF].

Besides, beyond figuring a city's outlook, 3D models can be used as interfaces -a sort-of 3D implementation of the GIS paradigm. An early attempt on the internet was carried out by [START_REF] Heinonen | An Information database for VRML Cities[END_REF] who developed what they call an Information database for VRML Cities, an interactive 3D model that can be queried interactively in order to retrieve information about services, shops, etc. We also applied this principle in early developments on the city of Kraków [START_REF] Blaise | SOL: Spatial and historical web-based interface for On Line architectural documentation of Kraków's Rynek Główny[END_REF], where the data we had gathered on each individual edifice or urban space was available using a 3D, non-photorealist model of the city. An interactive slider was used to browse through time, monitoring the content of the 3D model in real time. A number of graphic codifications were introduced in order to convey information about the nature of the documentation behind each component in the model, or about the nature of the hypothesis made in the reconstruction. The above mentioned Virtual Leodium project reinterprets this principle in a more contemporary technological suite: the objective behind the project is not only reconstructing the city, but also giving access to the historical evidence behind each edifice in the 3D model. Shortly said, to this day a clear evaluation of the performance (in terms of information retrieval) of such platforms still needs to be made.

With time passing by, and technologies reaching a higher level of accomplishment, virtual reconstructions tend to become primarily a media targeting general communication goals. We have been witnessing for the past decade a clear move form 3D modelling (used to produce images of past cities, and to test hypothetical reconstructions) to what could be called visual storytelling. Such initiatives, backed up by technological breakthroughs such as haptic interfaces, virtual and augmented reality (see for instance [START_REF] Dima | Touching the Past: Haptic Augmented Reality for Museum Artefacts" In Virtual, Augmented and Mixed Reality[END_REF] tend to borrow the visual language (when not the actual graphic engine or software suite) of computer games. They end up on with "visual products" that range from interactive 3D scenes to videos or serious games. The issue at stake for scientists is then to use other media in order to compile, memorise, and pass on the scientific basis behind such products. This is exemplified on our test field, the city of Kraków, by a research initiated on the occasion of 750th anniversary of the city's foundation. A significant multidisciplinary research effort was conducted in order to back up scientifically the production of a 3D model showing the city around 1650. Outputs include on one hand a series of very convincing communication products (videos, images, CD-Rom) and on the other hand scientific publications summing up the actual historical evidence on which hypotheses are built [START_REF] Marek | Cracovia 3D -Digital reconstructions of the historical built-up areas of Kraków[END_REF], Firlet 2010, Rydzewski 2006, and others). Unfortunately, in many cases, such a comprehensive effort to pass on the making-of a 3D model is neglected.

In short, there is a potential pitfall for knowledge sharing in initiatives that focus not on the data and its interpretation process, but rather on fostering a sort-of artistic freedom, legitimate in the context of a communication-oriented activity, but endangering scientific legitimacy.

A major concern for actors involved in the creation of virtual 3D cities today is therefore the scientific and technological "sustainability" of the end products, and in parallel their growing dependence, including in terms of work processes, to tools and software suites. As an answer, a number of initiatives have flourished in order to try and apply "open science" approaches and solutions -typically, developing standards such as CityGML [START_REF] Lorenzini | Semantic approach to 3d historical reconstruction[END_REF] or BIM (Building Information Modelling) approaches [START_REF] Baik | Integration of Jeddah historical BIM and 3d gis for documentation and restoration of historical monument[END_REF].

Yet in this chapter we wish to focus on more fundamental challenges: underlying methodological issues. Four main aspects are discussed below, with no ambition for exhaustiveness: uncertainty, role of the time parameter, memorising inferences and reasoning on collections.

The uncertainty issue

Dealing with uncertainty in the process of reconstruction of a "lost city" is regularly quoted as a background issue in the scientific community. [START_REF] Sylaiou | Virtual reconstructions in archaeology and some issues for consideration[END_REF] put it this way: "the main problem is that advanced graphic systems that are used for computer reconstructions may sometimes be too realistic. Things can be difficult, especially when they are based on partial evidence, but nevertheless suggest an impression of good knowledge of the past. [...] A very good 'image' can give the impression to the viewer that archaeologists know more than they actually know. Some products of computer reconstructions can be considered as scientifically accurate, because they seem to be accurate".

Back in 1999 [START_REF] Strothotte | Visualizing knowledge about virtual reconstructions of ancient architecture[END_REF] already picked up the issue and proposed to "encode systematically more information about the model than just its geometry" and then to "produce non-photorealistic images which encode this additional information". In our first experiment on Kraków (1999) we backed up the idea by differentiating systematically the existing form the hypothetical through graphic encoding (textures and transparencies,Fig1,left). But what we have learnt over time is that there is nothing like a "general", "overall" uncertainty: there are different factors of uncertainty: credibility of sources, precision, poor temporal density, contradictory data, and so on. Our claim is not that one should avoid representing objects that are ill-known, but that it is vital if a 3D reconstruction is to be reused scientifically, to keep track of all we know -including what we do not know, what we partially know, as well as what we infer from analogies and generic knowledge [START_REF] Blaise | From artefact representation to information visualisation: genesis of informative modelling[END_REF]. This means making a significant effort in formalising and passing on our doubts. The following list gives definitions of some of the notions that can be used in order to better differentiate uncertainty factors (partial list, includes the origin of the uncertainty).

Reliability /credibility (Origin: Sources)

A judgment made by the human consumer of the information about the information source… An information source that produces data that conflict with other data, has produced unreliable data in the past, or is otherwise suspect for some reason leads to uncertainty. [START_REF] Skeels | Revealing uncertainty for information visualization[END_REF] Imprecision (Origin: Sources and interpretation)

Inexactness of measurement [START_REF] Thomson | A typology for Visualizing Uncertainty[END_REF]. By extension, can apply to factual eye witness reports.

Incompleteness

(Origin:Sources) Information available to analysts is never complete. Even with excellent collection capabilities, observed evidence is likely to only be a small portion of the whole. (Thomson et Table 1. Definition and origin of some notions that can be used in order to better differentiate uncertainty factors (partial list).

Historical research is clearly a relevant test field when wanting to investigate the uncertainty issue, yet the topic is scarcely at the heart of research works. By contrast it is already a hot topic in information sciences as exemplified by [START_REF] Zuk | Theoretical Analysis of Uncertainty Visualizations[END_REF], or [START_REF] Gschwandtner | TimeCleanser: A Visual Analytics Approach for Data Cleansing of Time-Oriented Data[END_REF].

The time parameter issue

Reconstructing 'lost cities' is not only, and not even mainly, a matter of spatial distribution, of geometrical shapes: it is a matter of time. Handling the time parameter as such is, even in information sciences, an issue that remains scarcely addressed, although recent contributions like [START_REF] Aigner | Visualization of Time-Oriented Data[END_REF] help pushing it towards the top of the research agenda. In the context of historical sciences the issue is naturally crucial: we shall here mention two (and only two) bottlenecks we think actors involved in the analysis of 'lost cities' should be very conscious of: temporal consistency and the specificity of temporal data.

Ensuring the geometrical consistency of a 2D or 3D reconstruction is challenging because of the nature of the underlying data -repositioning of old maps is a typical example. But the same difficulty, although sometimes unsaid, exists when wanting to ensure the temporal consistency of a reconstruction. Quite often, the historical hints we handle do not permit to be sure of temporal co-occurrences of objects we represent in a single, synchronic view of a city (e.g. no direct evidence that two artefacts co-existed at time t). Even when we do have corroborated evidence that artefacts A and B coexisted at time t, we are often forced, due to lacking information, to represent A basing on information we have on A at time t -γ and B basing on information we have on B at time t + δ. There are some famous such anachronism in the cinema industry -a classic example is gladiators wearing watches.

A second bottleneck -and from our view even more prominent that the consistency issue -is understanding the nature of temporal data, and therefore providing analysts with means to perform reasoning tasks that are specific to the time parameter: spotting cycles, densities of changes, overlapping time slots, potential causal chains, managing uneven time granularities and branching time, uncovering significant trends such as speed of changes, or exceptions such as periods of intensive destructions, etc.. This implies primarily a conceptual modelling effort, building on notions that have stemmed from the information sciences community. This effort needs to be followed on from within historical sciences.

At this stage some precautions can be taken in order to minimise the impact uncertain or illdefined temporal indications at various stages of the research process (conceptual modelling, data management, reconstruction itself):

▪ distinguish uncertainty concerning the geometrical aspects from this concerning the dating,

▪ record the real data, independently of the choices and hypotheses we need to make before a reconstruction (e.g. if evidence is available for 1658, and the reconstruction shows 1700, record 1658, and the inference made that it was "probably" unchanged in 1700),

▪ switch from a synchronic approach (i.e. corresponding to a time point) to a diachronic approach, where the focus is put on transformations (time intervals) rather than on states (Dudek and Blaise 2010),

▪ finally, when possible, inform the users visually about temporal inconsistencies in the 3D model itself [START_REF] Blaise | New experimentation of a generic framework for architectural heritage data visualisation[END_REF]. Memorising choices: the "why" question:

Historical research starts with the cumbersome tasks of pulling together fragmental and heterogeneous evidence that will act as inputs in an analysis process. What is more processing these inputs requires numerous interpretation steps. Hence a huge potential information loss if the only result passed on to others is a 3D model, without indications about why the 3D model is what it is, about the inferences made by analysts during their study of the city (e.g. critical analysis and selection of sources, analogies used, generic knowledge called in, archaeological findings considered).

"Images" are easy to understand, and therefore simple to share with a wide public. 3D reconstructions of how that city could have looked like at this or that period, act as an interchange point where an interpretation process carried out by "the ones who know" (scholars, researchers, etc.) are made available for others in a form that is expected to be easily readable, and most often turns out to be assertive.

But what exactly does a 3D model contain in terms of knowledge? Recreating the spatial layout of a city in the past implies numerous interpretation steps, numerous inferences. Considering 3D reconstructions (i.e. 3D model) as the only result of this process would be like reducing a whole research process to its conclusion. Thereby if no precaution is taken it may conceal selections of inputs, assessments of data quality made during the analysis, inferences, and choices. 3D models most often leaves the actors with the responsibility of memorising and passing on the research process itself [START_REF] Dudek | How was this done? An attempt at formalising and memorising a digital asset's making-of[END_REF]) -yet another methodological bottleneck. What is a 3D reconstruction, besides a one-shot visual production, if we do not give ourselves means to formalise, memorise and visualise more than the result of a process, if we neglect to mention the way it was achieved?

What is at stake here is not only transferring knowledge, or clarifying choices and inferencesit is a cornerstone of scientific practices: reproducibility and intersubjective verification.

From distributing individual components in space to reading a collection

Analysing a whole city does introduce a quantitative break when compared to a one-monument monograph: more edifices, or urban components at large, have to be taken into consideration. But the break is not only quantitative, it is also, and in our view primarily methodological.

Shortly said, on one hand the information gathered while studying a whole city concerns heterogeneous urban components (an edifice, as well as an open urban space) and on the other hand includes non-localised data (e.g. a new law enforcing changes on this or that component), contextual information (e.g. a plague and its consequences on the population), reports of significant events (e.g. sieges, floods, etc.). Passing on the evidence, reasoning on it, requires an approach (and visual tools) that go beyond distributing individual components in space.

A number of such approaches, applied to the analysis of a city's territory and changes over time, have been convincingly introduced in the InfoVis community. [START_REF] Slingsby | The Role of Layout and Order in Treemaps for Showing Spatial and Variation in House Prices[END_REF] for instance reuse a visual formalism called treemaps, introduced by (Johnson and Shneiderman 1991), for "showing spatial and temporal variation in house prices". And indeed their approach does allow a clear understanding of patterns of change in each district of a city, over time.

Focusing on the temporal aspect of the underlying data, the "Commuting Scales" experiment by [START_REF] Beaude | Commuting Scales. Cartographie dynamique d'accessibilité temporelle[END_REF] summarizes in an abstract way periodically recurring travel times inside a whole urban area. Yet another convincing example is A. Yabuuchi's "Home to School diagram" [START_REF] Yabuuchi | Home to school surrounds diagram[END_REF], a visualisation, inspired by musical staves, that turns an urban route into a series of individual scenes. For each scene components in the surroundings (vegetation, buildings, vehicles, etc.) are visualised through specific icons and help portraying something rather intangible -an atmosphere.

These examples illustrate a fundamental observation: visualising and reasoning on a collection is not only allowing for the analysis of "lots" of individual items, it means depicting, and analysing, the collection as such.

Analysing a whole city differs from analysing a "list" of individual components in the sense that it implies the analysis of relations components may have with one another and with a wider context. Introducing InfoVis practices that focus on sensemaking in such large information spaces appears as a promising research path. However it has to be said that most examples found in that community use "well-defined" data sets. As mentioned before, reasoning on the past of a city means handling of large, heterogeneous data sets, hindered by uncertainties. Bridging InfoVis-birthed approaches and the reality of historical research therefore remains an open challenge at large.

Sensemaking in historical research: an information visualisation perspective

Information visualisation builds on a specific interpretation of the term visualisation that today encompasses a wide range of practices. This interpretation was worded by R. Spence [START_REF] Spence | Information Visualization[END_REF] as follows: "visualisation is a cognitive activity". In other words, visualisation here clearly targets understanding -it is not a result but a means to perform reasoning tasks.

Information visualisation is defined in [START_REF] Kienreich | Information and Knowledge visualization -An oblique view[END_REF] as "the use of computer-supported, interactive visual representations of abstract data to amplify cognition". M. Friendly [START_REF] Friendly | A brief history of data visualization[END_REF]) considers the discipline as inheriting from the historical development of on one hand statistical graphics and data visualization, and on the other hand thematic cartography.

Information visualisation is today an active research area, with however still rather scarce applications in historical research, although hot topics like time-oriented data, or handling "dirty data" can be seen as potential methodological bridges with the reality of historical research.

In this contribution we do not intend to discuss of information visualisation as such, but rather wish to illustrate through a chronology of experiences how visual tools inspired by that discipline can be profitable when facing the four major bottlenecks we have discussed above: uncertainty, time parameter, memorising choices, and reading collections as such. The experiences that are reported below share a number of common choices in terms of conceptual modelling as well as in terms of computer infrastructure:

▪ urban components (edifices, urban blocks, streets, squares, etc.) are modelled as one unique "being" with potentially several successive morphologies, ▪ the model includes typologies classifying on one hand states (a morphology and a time slot during which it is believed to have remained stable) and on the other hand transformations used to qualify what changes occurred and how long they took [START_REF] Dudek | Profiling artefact changes: a methodological proposal for the classification and visualisation of architectural transformations[END_REF]), ▪ components are not considered as having disappeared until confirmed evidence can be found that states they have been fully dismantled (underground structures included),

▪ qualitative lexical scales are used to formalise various types of doubts arising about the lifeline of components, uncertain morphology, materials, functions, durations, etc., ▪ all pieces of data are stored in an RDBMS and XML files, ▪ the infrastructure's user interface is web-compliant (HTML produced on the fly),

▪ graphics (2D or 3D) are produced on the fly, as answers to user queries, in standard formats (mainly SVG -Scalable Vector Graphics).

Localising and interfacing historical evidence

Uncertainty, as mentioned earlier, affects both (and differently) the spatial and the temporal determinacy of a component. Focused on the former, one of our earliest experiments was an Information System called VIA. The system establishes a direct link between historical sources and urban components, and produces 2D and 3D visual displays used as interfaces [START_REF] Blaise | New experimentation of a generic framework for architectural heritage data visualisation[END_REF]. Each component can be queried in order to retrieve the information available on it, and vice versa any historical source can be queried in order to localise its "architectural content" in 2D or 3D. VIA gave us a first opportunity to dig into uncertainty factors (Fig 2,c). Each urban component is described by a set of "justifiers" -i.e. values representing our estimation of the reliability of sources concerning the morphology of the component, the construction material, the function and the dating. Besides, a comparative chronology of transformations of a given component and of historical sources helps underlining potential anachronisms (i.e. temporal gaps between a change and its report in sources) or factual errors.

The temporal aspects were still underrepresented in the VIA first developments, although time sliders included in the visualisation did help browsing through time. But this solution only provides "temporal snapshots" on the data: only one period is visible at a time. Comparative chronology of changes and a map of densities of changes over time (Fig2, a) prefigure solutions we investigated since that early experiment in order to spot and analyse temporal patterns.

A later development of the VIA platform targets specifically visual sources that cannot be unambiguously localised using contemporary methods because of their artistic nature, because of lacking information on the captors, or because de facto they correspond to several points of view (e.g. historical panoramas). By contrast the Locus Imaginis project [START_REF] Stefani | A Web Platform for the Consultation of Spatialized and Semantically-Enriched Iconographic Sources on Cultural Heritage Buildings[END_REF] illustrates an ambition to localise visual sources in the space of a 3D model, but focuses on well-defined visual sources. On what solution can the analyst base when facing old paintings, hand-drawn sketches, panoramas? The idea we have investigated in the VIA platform was to describe an approximate point of view using a combination of parameters: the viewer's estimated position(s) (x,y,z), an estimated target point(s), a horizontal angular direction(s) of view, a geographical bearing(s), a vertical bearing(s), the image's ratio and type (Fig 2,d). The approach allowed us to illustrate some noteworthy observations, typically when a painting turns out to correspond not to a real view but to a combination of several points of views carefully chosen by the painter to reach a satisfactory artistic result [START_REF] Dudek | Visual tools decipher historic documentation[END_REF].

Understanding temporal patterns

Understanding how transformations of a city develop over time, and not only in space, is naturally a key aspect of historical research. The InfoVis community has been very active in the formalisation of time as such, with the introduction of models aimed at coping with notions like cycles, time granularity, density, determinacy (etc.) implemented on real cases. Temporal uncertainty has been addressed, for instance in the PlanningLines experiment [START_REF] Aigner | PlanningLines: novel glyphs for representing temporal uncertainties and their evaluation[END_REF] where time intervals are modelled with "floating" bounds in order to allow the assessment of risk of delays in the planning of chained activities. A similar mechanism was introduced in the chronographs project through which we introduced a methodological framework aiming at the description of life cycles in a diachronic approach [START_REF] Dudek | Understanding changes in historic architecture. Can we provide tools & methods for visual reasoning?[END_REF]. Here focus is put on the way artefacts get transformed, with a grid of notions identifying life cycles as a sum of states and transitions. Chronographs act as visual explanations (a tribute to Tufte 1997) of the artefact's life cycles, underlining temporal patterns of evolution within a site or across sites, but also underlining uncertainty of temporal bounds. They combine three elements: diachrograms and variograms that allow a global view on transformations, and features variation visual assessments that foster comparisons and the reading of consequences. The whole disposal is designed to combine vertical readings -"what precisely happens at period p" -and horizontal readings "how does a feature change with time". In that sense, the disposal matches Bertin's view of graphics as "visual answer to a question" [START_REF] Bertin | Semiology of Graphics: Diagrams, Networks, Maps[END_REF].

Understanding alternative temporal patterns

The chronographs solution has proven quite efficient in performing reasoning tasks -it does help assessing causal relations and orders in time sequences, events and consequences in a robust manner. But chronographs have the pitfall of forcing the analyst to choose one and only one scenario of evolution for a given urban component -in other words it does not identify those key historical time slots for which the analyst has interpretation difficulties. In addition although doubts about the dating are duly visualised, no mean is given to say that the very existence/relevance of an event is questionable. As an answer, we developed a new set of visualisations that capitalize on the user's a-priori understanding of the timeline paradigm, but introduce visual interruptions marking key choices the analyst has to make before adopting an unambiguous scenario [START_REF] Dudek | Analyzing Alternative Scenarios of Evolution in Heritage Architecture: Modelling and Visualization Challenges[END_REF]. Three complementary graphics are produced, corresponding to different analysis needs: These graphics help highlighting alternative explanations that can arise from the available data. However they have their pitfall too: they remain a solution putting "side by side" individual cases. Considering we studied in this experiment a collection of 27 artefacts, Tufte's recommendation "enforce comparisons within the eyespan" was a challenge. We decided for a visualisation more or less inspired by the "small multiples" principle (concept attributed to Scheiner's 1626 representation of changes in sunspots over time -see [START_REF] Friendly | A brief history of data visualization[END_REF]. Life spans, the number of transformations, and the number of alternatives across the whole collection are visualised in a single graphics, helping the analysts to read the collection of artefacts as a whole.

Communicating about doubts

It is sometimes said that conveying doubts is irrelevant in the context of a communication effort. In an attempt at contradicting what we consider as a simplistic view, we have introduced an edutainment-oriented proof-of-concept prototype called tangible chronology [START_REF] Blaise | A tangible chronology[END_REF]. This prototype combines a master board, 3D physical models of the artefacts, with a coding of their position on the board and in ordinal time, and a tangible timeline for each artefact. Its specificity lies in tangible codifications used for various purposes, from positioning 3D physical models on the master board to reliability assessments. The initial concept was to offer users, including ill-seeing users, means to analyse the site's urban composition and evolution, for any time slot inside the 750 years covered. To do so users combine on the master board 3D physical models corresponding to each edifice's evolution at the period chosen. But what the experiment did underline at the end of the day is that consistency with the underlying historical evidence's specificity (temporal aspects, uncertainty) does not undermine scientific communication, it helps it.

Reasoning on space and time in a row

There are a number of reasons that can be pushed forward in order to explain why it is arduous to combine the reading of spatial and of temporal patterns in one unique visualisation. At the end of the day, whatever scale is concerned, visual solutions used to represent spatial features (in 2D or 3D) and temporal features are in most cases simply put side by side -typically a map or 3D model, complemented by a time chart like in [START_REF] Rød | ViewConflicts: Software for Visualising Spatiotemporal Data on Armed Conflicts[END_REF], [START_REF] Stefani | Reasoning about space-time changes: an approach for modeling the temporal dimension in architectural heritage[END_REF]) [START_REF] Auer | HerbariaViz: A web-based client-server interface for mapping and exploring flora observation data[END_REF] or [START_REF] Tomaszewski | Geovisual analytics to support crisis management: Information foraging for geo-historical context[END_REF].

The ConcentricTime visualisation [START_REF] Blaise | Concentric Time: Enabling Context + Focus Visual Analysis of Architectural Changes[END_REF]) is by contrast an attempt at reading in a row the spatial distribution and the changes over time of a collection of artefacts. It capitalizes on basic, well-known, well understood representations (cartography, timelines) and introduces a specific, context+focus, graphic combination of spatial features and chronology.

A map in the central part of the visualisation shows the layout of artefacts. Each artefact is connected with a radiating timeline along which its transformations are localised in time.

Moments of change on the timeline, represented by coloured rectangles, can be interactively queried: the 2D contours corresponding to the user query are then projected in the central area.

Because contours are drawn with a level of transparency, this mechanism enables usermonitored comparisons of contours such as neighbourhood analysis or transformation analysis (e.g. period of emergence of a given component).

The visualisation allows the reading of an individual artefact's lifeline, and fosters the reading of common behaviours inside the collection of artefacts (impacts of changes on one artefact on others, general patterns of change such as 19th century destructions, etc.)

ConcentricTime was designed in order to combine inside a unique information space, spatial features and chronology, with as constraints uncertainty assessment, interface capabilities, and simplicity. As a result, although limited by the fact that only one scenario is shown, and that the number of radiating timelines is finite, the concept does provide efficient support in carrying out reasoning tasks about architectural changes on a collection of artefacts, and appears as fairly generic (Fig 4).

Making the best of an ill-defined data set

In a recent experiment [START_REF] Blaise | Can simplicity help?[END_REF] we focused on very poorly documented edifices: wooden stalls that are known to have existed from textual sources, but for which no visual material is available. These commercial facilities share rather challenging particularities:

▪ They cannot be precisely localised (known only in archival sources by expressions such as "close to the town hall" or "located in the northern sector"). Moreover, they were wooden structures, demolished during the 19th century. There is accordingly no archaeological indication we can count on.

▪ No direct visual or textual archival material can be found that would help analysts say what were their construction and spatial layout. In fact, these facilities may even not have been "buildings" in the proper sense: they could in theory even have been rows of movable stalls, not physically connected to one another, but considered as a consistent group basing on their common function (goods/services sold).

If very little is known about these commercial facilities (in fact temporal aspects are better known than spatial aspects, which is not that common), we do have one document that gives useful indications: an 18 th century inventory conducted by Kraków's municipal authorities of the time. The challenge we were facing was then: can we learn anything useful on the layout or organisation of these facilities basing in this only document? As an answer, we re-interpreted two classic 18th century visual formalisms -poleometric tables and candlestick charts (Fig 5).

Ultimately some noteworthy patterns were uncovered such as no relation of tax levels to surfaces, no catching-up process in the tax policy, regularities inside a consistent group of stalls with few contrasting components and so on.

This re-vision of classic visualisations did show the potential of InfoVis-inspired solutions when facing ill-defined data sets, and particularly how such an approach can facilitate workgroup discussions, unveil unexpected trends in data set previously considered as fully investigated, and in the long run uncover new research questions.

Collection reading visualisations

One of the key services expected from InfoVis solutions is to provide the analyst with tools that will help him cope with large information spaces, and uncover trends or exceptions that are simply not visible at first glance. This naturally goes for the spotting of "outliers" in a collection (may the 'distance' of the item from the rest of the collection be the result of faulty data, or a genuine difference) as well as for the spotting of general trends. From the practical point of view, this implies promoting visual solutions that implement a well-known mantra in the InfoVis community, worded by B. Schneiderman as follows: "Overviews first, details on demand". It also implies, when needed, introducing grouping mechanisms that analysts consider as relevant for this or that reasoning purpose.

An example of this approach is the evolution field metaphor we introduced in order to analyse the spatial distribution of types of artefacts by "clusters". The objective was to get a quick idea of whether groups that are consistent in space are also consistent in time, in patterns of evolution, in density of sources, etc. A multidimensional icon sums up various parameters: possible period of construction, overall lifetime, possible period of demolition/dismantling, confirmed or suspected events like fires, possible or definite transformations, archaeological remains of (or attributed to) the artefact. Icons are combined with regards to a given analysis need. The approach was applied for instance on Kraków's market square ensemble in order to weigh the density and specificity of objects on both sides of the Cloth Hall. Wooden commercial facilities on the west side outnumber by far those on the east side, some emerge earlier in time, their process of decay and demolition stand out as harder to date precisely -in fact activity as such appears as far greater on the west side (Fig 5 ).

Another example of the approach are multidimensional transformation pie charts organised in temporal clusters [START_REF] Dudek | Analyzing Alternative Scenarios of Evolution in Heritage Architecture: Modelling and Visualization Challenges[END_REF]. Here multidimensional icons of varying complexity are arranged visually either as classic time series or as small multiples (Fig 5). They help observing the data and its interpretation in a renewed way, typically highlighting source effects like the relation of the construction type to the nature, amount and assertiveness of the pieces of information available.

It is important to state that such visualisations show that there is room for comparisons and reasoning even when edifices for instance cannot be precisely localised in space -heterogeneity in terms of level of knowledge naturally remains a concern, but ceases to be a lock.

Context assessment and temporal co-occurrences in a collection

The last experience we mention aims at putting architectural transformations into a context, and at highlighting of temporal co-occurrences. Among uncertainty factors hindering the analyst's reasoning process about the city and its transformations are potential results of events and facts that cannot be directly linked to this or that urban component (e.g. legislation, occupation by a foreign army, plagues, demographic variations, presence of important people, etc.).

If we are to support an analyst in his effort to understand and recount the evolution of a city, we definitely need to go beyond the depiction of consequences -i.e. spatial changes at time t, and correlate these changes with potential causes -or at least with a more general context. This is precisely the aim of the historySkyline visual metaphor. The visualisation pulls together in a time-oriented display the data we have on transformations of urban components (along with their uncertainty assessment and with the amount of sources used to document the changes) and a number of contextual indicators (rulers, military events, natural disasters, legal matters, global military context in the country, demography).

The design of the visualisation builds on the concept of visual metaphor, described by [START_REF] Kienreich | Information and Knowledge visualization -An oblique view[END_REF]. In practice it builds on the metaphor of an urban skyline, with the horizon line acting as a timeline (time goes from left to right). Shortly said, the building activity (changes) is represented as "blocks" or "facades", and elements of contexts are superimposed on them.

At this stage the historySkyline visualisation is basically a proof-of-concept prototype, needing further development, but it appears as promising in identifying temporal co-occurrence patterns -expected or not (see [START_REF] Blaise | Spotting temporal co-occurrence patterns: the historySkyline visual metaphor[END_REF].

Conclusions

Our record of experiences illustrates how we can today complement "conclusive" visual results such as 3D reconstructions with graphics aimed at supporting reasoning tasks on the data behind the analysis (e.g. at clarifying choices, considering alternatives, cross-examining the historical evidence, assessing contexts, interrelations, potential causal chains, etc.). Shortly said, it underlines the potential benefits of InfoVis-inspired abstract graphics as means to dig into ill-defined data sets, get aware of relations between the data, and investigate the time parameter. We have in particular discussed four major scientific challenges that the growing use of 3D models in the study of "lost cities" raise: dealing with the ill-known, reasoning on temporal data, ensuring the reproducibility of work processes, enabling the analysis of collections as such.

At the end of the day our research underlines methodological issues that intersect information sciences, and historical sciences. In that context, modelling and visualising doubts, or memorising research processes, remain issues to be further investigated. Understanding the time parameter as multidimensional (not only running from past to future, but needing to be described in terms of densities, rhythms, alternative paths, etc.) is indeed a challenge to come. Finally, the quantity and heterogeneity of data sets and of urban components concerned when analysing a whole city implies questioning the way we today handle collections.

Our record of experiences on Kraków shows that exploring visually the known and the illknown about a city's evolution can benefit from intersecting the above mentioned scientific fields, provided the nature of the historical evidence is considered as a research's cornerstone.

  al 2005) Lineage (Origin: Sources) Conduit through which info passed (number of steps). (Thomson et al 2005) Approximation (Origin: Sources and interpretation) Attempt to come close to measuring or describing a phenomenon when we cannot measure or describe it with perfect precision. (Skeels et al 2010) Timing (Origin:Sources) Temporal gaps between occurrence, info collection & use. (Thomson et al 2005) Subjectivity (Origin: Interpretation) Amount of private knowledge or heuristics utilized. (Zuk and Carpendale 2007) Inconsistency (Origin:Sources) Extent to which info components agree (5 say M; 2 say T). (Thomson et al 2005) Accuracy (Origin:Sources)Difference between observation and reality.[START_REF] Thomson | A typology for Visualizing Uncertainty[END_REF]

Fig 1 .

 1 Fig 1.Left, virtual reconstructions of the town hall ensemble. Existing parts, (i.e. the belfry walls as they remain today) is differentiated visually from the hypothetical parts (represented in colour). Right, the VIA platform investigates the use of non-photorealistic 3D models as interface. Top, transparencies inform on confidence levels, a slider allows user-monitored browsing through time -each artefact can be queried (lifeline, bibliography, …). Bottom, colour and emissivity are used to spot in a scene corresponding to a period t, shapes that correspond to an earlier or later phase of evolution. [ I. Dudek & J.Y. Blaise, UMR CNRS/MCC 3495 MAP]

  Fig 2. a) On the left a slider allows user-monitored browsing through time (here on a subselection of components, artefacts only). This slider is also used to show densities of changes over time: each little horizontal bar corresponds to a change in one of the components under scrutiny. Periods of high and low activity are revealed. b) Graphical codification of justifiers and comparative chronology of changes. c) Successive layouts of the town hall are superposed using transparencies, underlining the density of land use over time. d) Glyph used to position in space visual sources qualitatively. [ I. Dudek & J.Y. Blaise, UMR CNRS/MCC 3495 MAP]

Fig 3 .

 3 Fig 3. Graphs of potential interactions position changes in ordinal time, and allow for the visual assessment of alternative scenarios of evolution. Dark circles and rectangles correspond to known states. Triangles position events that result in temporal "forks", i.e. moments when alternatives scenarios should be considered. Dotted lines above the triangles mean the event is NOT confirmed (a, b, d). Dotted lines below the triangles correspond to alternative potential consequences. The graphs are read as follows: a), b) and d) the event may not have occurred at all (triangle upwards, dotted line straight to next step) but if it did occur (triangle downwards) either it has had limited consequences (light grey circle) or it lead to a main change (black circle, rectangle with question mark). Outlined circles correspond to destructive changes. c) confirmed alternative: the event did occur for sure (triangle downwards) but either it has had limited consequences (light grey circle) or it lead to a main change (black circle, rectangle with question mark). Graphs are presented along with explanatory vertical texts, as in the rightmost example. [ I. Dudek & J.Y. Blaise, UMR CNRS/MCC 3495 MAP]

Fig 4 .

 4 Fig 4. Principle of the ConcentricTime visualisation. Top left, artefacts are connected to radial timelines (a, a') that distribute transformations in time. Colours differentiate event types: yellow (periods of stability, no known change, f), blue (morphological change, including construction, k), red (functional change, d), grey (destruction, c, meaning here that no visible trace is left above the ground). Shapes differentiate duration and certainty: long-lasting events (duration > year, rectangles -i, e, k), punctual events (duration < a year, circle -d, j), uncertain dating white filling and outline (i, j), hypothetical dating dashed outline (e, g). Top right, contours can be projected inside the central circle on user selection, enabling user-monitored comparisons (neighbourhood analysis for instance). Bottom, the visualisation can be used in "focus view" so as to allow a fine grain analysis of temporal patterns across a group of artefacts. Illustrated here is the town hall ensemble: a majority of temporal co-occurrences for artefacts a and b (Granary/Town Hall, black arrows), a majority of non co-occurrences for artefact d (prison) with neighbours b and d (town hall, belfry, green arrows), a phase impacting all the elements (purple arrow). Bottom right, the visualisation can be used in "context view" so as to spot patterns concerning the whole collection -here the massive destruction phase on the Market Square during the 19th century (only here artefacts, a, remain until now).

Fig 5 .

 5 Fig 5. Abstract visualisations designed to facilitate the analysis of collections. Top, a re-vision of M .Homma's candlestick charts is used to represent the relation of tax levels to surfaces in a group of comparable commercial stalls: "outliers" are easily spotted.Middle, the evolution field metaphor use to characterise the contrasting behaviours of artefacts located on the West and East sides of the market square. Bottom, multidimensional icons summarise characteristics of an artefact (here concerning transformations). They are then grouped into user-defined "temporal clusters" (represented by columns) -here a column corresponds to one century. Rhythms and general trends inside and across clusters can be spotted: the most important building activity on the market square in Kraków takes place during the 14 th century, brick and stone buildings tend to be built earlier, wooden structures appear as harder to date and come in a second row, … [ I. Dudek & J.Y. Blaise, UMR CNRS/MCC 3495 MAP]

[ I. Dudek & J.Y. Blaise, UMR CNRS/MCC 3495 MAP]


Duriot Robin
email: robin.duriot@ensam.eu

Frayssinhes Rémy

Rescalvo Francisco

Collet Robert

Denaud Louis

Girardon Stéphane

Pot Guillaume

Cottin Fabrice

Butaud Jean-Claude

Propriétés mécaniques en flexion de LVL de gros douglas

NRFacteur•

  Directions données pour l'utilisation du duramen : • Travail d'homogénéisation de la répartition des défauts (nodosité, variation de pente de fil, …) dans le matériau : modèle numérique pour diminuer les écarts-types afin d'augmenter les valeurs caractéristiques • Classification des placages par résistances nécessaire pour augmenter les valeurs moyennes et caractéristiques de produits lamellés issus du déroulage de douglas pour des ponts et autres solutions constructives mixtes bois-béton collés » Nervures de bois Ressource de douglas locale Gros bois (Ø > 50cm) => défauts importants Valorisation en LVL Recherche d'optimisation des plis par orientation et qualité Aubier et duramen de douglas, Kerto ® S pour vérification Valeur caractéristique du Kerto ® S équivalente à la valeur du fabricant sans application du facteur correctif de taille, inférieure après son application • Résistance de l'aubier de douglas du même ordre de grandeur que le Kerto ® S • Résistance du duramen 55 % inférieure à celle de l'aubier Comparaison poutres mères/filles (b m = 120 mm / b f = 45 mm) • Poutres filles 36 % supérieures en résistance moyenne par rapport aux poutres mères (31 % en valeur caractéristique) • Plus grande variabilité des valeurs de résistances des poutres filles • Valeurs caractéristiques après application du facteur correctif de taille sensiblement équivalentes (15,83 MPa pour les poutres mères, 13,42 MPa pour les filles) Duramen préféré en extérieur: résistant aux attaques biologiques Essais sur chant Densités • Bonne correspondance densité/rigidité générale • Pour aubier/duramen, correspondance densité/résistance • Kerto ® S résistant / à sa densité : purgé et trié • Module local systématiquement plus élevé que le module global : déformation de cisaillement non prise en compte dans le global (et matériau homogène sans défaut concentré localement) • Module global d'aubier 15,5 % plus élevé que celui du Kerto ® S • Module global de duramen seulement 5 % plus élevé que le Kerto ® S • Modules filles/mères équivalents (dispersion plus élevée pour les filles)

Ces travaux ont été menés à bien grâce à la Plateforme Technique Xylomat subventionnée par l'ANR-10-EQPX-16 XYLOFOREST.


Kazem Ardaneh
email: kazem.arrdaneh@gmail.com

Remi Meyer

Mostafa Hassan

Remo Giust

Chen Xie

Benoit Morel

Ismail Ouadghiri-Idrissi

Luca Furfaro

Luc Froehly

Arnaud Couairon

Guy Bonnaud

Francois Courvoisier
email: francois.courvoisier@femto-st.fr

High energy density plasma mediated by collisionless resonance absorption inside dielectrics

We demonstrate for the first time to our knowledge the generation of overcritical plasma densities inside transparent solids over long distances using femtosecond laser pulses. This opens new avenues for high energy density physics in confined geometry such as warm dense matter study or the synthesis of new material phases. We show both with experiments and first-principles simulations, that femtosecond conical interference via a Bessel beam creates a dense plasma rod with typically 100 nm diameter in sapphire. The interaction is in ideal conditions to trigger collisionless resonance absorption. This mechanism plays a primary role in the energy deposition process, yielding a plasma with an energy density on the order of MJ/cm 3 and a length that can reach several cm using only tabletop femtosecond lasers.

Extreme focusing of a femtosecond laser pulse with numerical apertures in excess of unity inside transparent materials generate a nanosphere of dense plasma, but the volume of the excited material is too small for X-ray investigation of warm dense matter [START_REF] Guillot | Interiors of giant planets inside and outside the solar system[END_REF][START_REF] Saiz | Probing warm dense lithium by inelastic X-ray scattering[END_REF] or for the synthesis of new material phases [START_REF] Vailionis | Evidence of superdense aluminium synthesized by ultrafast microexplosion[END_REF][START_REF] Smillie | Exotic silicon phases synthesized through ultrashort laser-induced microexplosion: Characterization with Raman microspectroscopy[END_REF]. Reducing the focusing strength enlarges the focal volume, but -in contrast with laser interaction at the surface of solids -the plasma density build-up inside the solid defocuses a Gaussian beam so that high plasma densities cannot be reached, even with higher pulse energy. The problem is illustrated in Fig. 1(a): after plasma generation on the optical axis by the initial part of a laser pulse, the trailing part of the pulse impinges on the plasma with a high angle of incidence i with respect to the plasma surface normal. Instead of heating the plasma core, the optical pulse is deviated outwards to the regions with higher refractive index, even for very low plasma densities. This is the wave-turning phenomenon [START_REF] Kruer | The physics of laser plasma interactions[END_REF][START_REF] Eliezer | The Interaction of High-Power Lasers with Plasmas[END_REF] which presents a fundamental challenge. Importantly, the most intense components of a Gaussian beam, at the center of its far-field distribution, have largest incidence angles. They turn away at the largest distance from the plasma center [see circled inset in Fig. 1(a)]. Due to the wave-turning, plasma generation continues outside the initial volume and consequently the plasma remains sub-critical, i.e., below the critical density at which the plasma permittivity turns to zero, and the deposited energy density remains low [START_REF] Bulgakova | Modification of transparent materials with ultrashort laser pulses: What is energetically and mechanically meaningful?[END_REF][START_REF] Naseri | Mechanism of laser induced filamentation in dielectrics[END_REF].

In this article, we report the creation of over-critical plasmas along quasi-arbitrary distances with femtosecond Bessel beams in sapphire, using only a moderately high numerical aperture (0.4). The plasma absorbs high amount of the pulse energy as a result of the resonance absorption mechanism, observed here for the first time in the bulk of solids.

A zeroth-order Bessel beam is a circularly-symmetric interference field, so-called diffraction free [START_REF] Durnin | Diffraction-free beams[END_REF], whose length is independent from the central lobe diameter [Fig. 1(b)]. Its conical structure uniformly distributes energy by a transverse flow along the plasma created in the central core. Resonance absorption has been widely studied within the context of inertial confinement fusion, by illuminating the surface of solids [START_REF] Gibbon | Collisionless absorption in sharp-edged plasmas[END_REF][START_REF] Teubner | Angle-dependent X-ray emission and resonance absorption in a laser-produced plasma generated by a high intensity ultrashort pulse[END_REF][START_REF] Palastro | Resonance absorption of a broadband laser pulse[END_REF]. It occurs when a laser pulse obliquely impinges on a plasma ramp and the laser electric field has a component parallel to the plasma density gradient. In this condition, mode conversion resonantly drives electron plasma waves at the critical surface. This can transfer up to 70% of the laser energy into the plasma [START_REF] Kruer | The physics of laser plasma interactions[END_REF][START_REF] Denisov | On a singularity of the field on an electromagnetic wave propagated in an inhomogeneous plasma[END_REF]. Mode conversion is efficient for the moderate incidence angle of Bessel beams on the plasma density ramp and generally inefficient in Gaussian beams because most of the energy is located on components at grazing incidence.

We determine the typical plasma profile by comparing complementary experimental diagnostics to firstprinciples Particle-In-Cell (PIC) simulations using the 3D massively parallel code EPOCH [START_REF] Arber | Contemporary particle-in-cell approach to laser-plasma modelling[END_REF] because direct measurement of the plasma density inside the bulk cannot be performed via optical techniques when the plasma reaches the critical density at sub-wavelength scales. We demonstrate that in sapphire, over-critical densities are reached over a typical radius of 75-200 nm with typically FIG. 1. Laser-plasma interaction within dielectrics. (a) Gaussian beams are conventionally limited to create sub-critical plasmas in dielectrics because of the wave-turning phenomenon. Most of the waves composing the Gaussian beam impinge on the plasma with a very large incidence angle: these are deviated away well before they reach the plasma center. The plasma buildup expands the plasma volume but the density remains sub-critical. The radius of the turning point rt is defined for an incidence angle i by the density reached n(rt) = nc cos 2 i, where nc is the plasma critical density. (b) In a Bessel beam, the far-field k-space spectrum is narrow, the whole pulse energy impinges on the plasma with a relatively low incidence angle. The steep plasma density profile generated by the pulse onset makes resonance absorption possible, which transfers energy from the laser beam into the plasma. The energy transfer and ionization are therefore extremely localized on a sub-wavelength rod. The geometry of the interaction is longitudinally invariant.

50% absorption of the laser pulse energy. This is additionally confirmed by the observation of second harmonic from the bulk of a centrosymmetric dielectric for the first time to our knowledge. While conventional models of laser energy deposition hitherto have relied on collisional absorption, we show here that most of the absorption is due to collisionless resonance absorption. Our findings open a new route to develop high energy density physics in a confined geometry inside solids, but also open new perspectives for nonlinear optics with epsilon-near-zero materials [START_REF] Alam | Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region[END_REF], synthesis of new material phases and laser material processing.

The interaction of an ultrashort pulse with a dielectric medium can be viewed as a two-stage process. In the first stage, field ionization and electron-impact ionization create a plasma, with which the trailing part of the laser pulse interacts during the second stage. Our experiments show that the femtosecond Bessel pulse generates a plasma over a length of 18 µm with a typical diameter of a few hundreds of nanometers and absorbs approximately 50% of the 1 µJ pulse energy (similar plasma was produced over a length close to 1 cm with mJ pulse energy [START_REF] Meyer | Extremely high-aspectratio ultrafast Bessel beam generation and stealth dicing of multi-millimeter thick glass[END_REF]). We point out that the ionization energy absorbed to produce an over-critical plasma of this size is n c V U g where n c is the critical density at 800 nm, V ≈ 1.5 µm 3 the plasma volume and U g ≈ 10 eV the bandgap of sapphire. The ionization energy is less than 0.04 µJ which is negligible in comparison with the total absorbed energy. We therefore hypothesize that the first stage is very short compared to the pulse duration and we focus our mod-eling efforts on the second stage of the interaction. Our model does not take into account ionization in order to isolate the laser-plasma interaction.

We first qualitatively describe the physics of Bessel beam interaction with plasma using numerical simulations. We have performed 3D PIC simulations to model the interaction of a 100 fs Bessel beam with a plasma rod. The pulse, with a central wavelength λ = 800 nm, propagates along z-direction and is polarized along the x-direction [START_REF] Ardaneh | Generation of a Bessel beam in FDTD using a cylindrical antenna[END_REF]. In the absence of plasma, the intensity reaches 6 × 10 14 W/cm 2 , as in the experiments. The beam cone angle is θ = 25 • , which corresponds to an incidence angle i = 65 • on the cylindrical surface of the plasma [Fig. 1(b)]. In the central lobe the amplitude of the z-component of electric field is 25% of the x-component, while the y-component remains negligible (2%). We have presented in detail our numerical scheme in the Supplemental Material [18]. In Fig. 2(a), we show the fluence distribution, i.e., the timeintegration of the Poynting vector of the Bessel beam, in xy-plane at a propagation distance corresponding to the peak of axial fluence profile, without plasma. In Fig. 2(b), the beam interacts with an over-critical circular plasma rod with a turning point radius of 274 nm. All lobes are shifted outwards by a distance of about 300 nm due to the wave-turning phenomenon (the slight discrepancy stems from the fact that the estimate of the turning point radius is made for a monochromatic plane wave).

In the zoom-in view presented in Fig. 2(c), two highintensity structures appear inside the region of the initial central lobe. One is composed of two electromagnetic lobes outside the plasma (y = ±0.5 µm), oriented perpendicular to the pulse polarization. They originate from the difference in permittivity between the plasma rod and the external medium [START_REF] Bhardwaj | Optically produced arrays of planar nanostructures inside fused silica[END_REF][START_REF] Liao | High-fidelity visualization of formation of volume nanogratings in porous glass by femtosecond laser irradiation[END_REF]. This effect occurs even for sub-critical plasmas. It reduces the amplitude of the field in the polarization direction and amplifies it in the perpendicular direction. The second structure is much more localized in the vicinity of the critical surface and shows two lobes along the polarization direction. It corresponds to resonantly driven electrostatic plasma waves at the critical surface. Therefore, this structure cannot be observed experimentally by beam imaging. This is why, in the following figures, we exclude the electrostatic field components from the simulated fluence distributions.

In Figs. 3(a)-3(d), we present experimental results of near field fluence imaging in 400 µm thick C-cut sapphire Al 2 O 3 . They have been obtained by collecting the 100 fs laser pulse after its interaction with the sample, using a single shot beam sectioning technique [START_REF] Xie | Tubular filamentation for laser material processing[END_REF]. We have detailed our experimental techniques in the Supplemental Material [18]. Figures 3(a We observe a significant energy drop of nearly 50% over an 18 µm segment of propagation, which corresponds to the region where plasma is generated. This is approximately the length of the void channel that is created in sapphire in single shot under similar laser illumination conditions [START_REF] Rapp | High aspect ratio micro-explosions in the bulk of sapphire generated by femtosecond Bessel beams[END_REF]. We independently checked that the energy drop is effectively equal to the total loss within the sample, confirming that energy deposition is localized in the high-intensity region, i.e., not in an earlier stage of the propagation as it can be the case for Gaussian beams.

Importantly, we observe in Fig. 3(c) that in the plasma region (z = 14 -32 µm), the surrounding lobes negligibly shift with respect to those in the regions where plasma is absent (z < 14 µm, z > 32 µm). This sets the upper limit to the turning point radius r t roughly to the experimental sensitivity associated with the width of the Bessel lobes, i.e., typically 500 nm. Given the incidence angle, the density at a distance r t is less than n c cos 2 i = 0.086n c .

In Figs. 3(a) and 3(c), the shift due to wave turning is invisible within the central lobe. Because of the limited numerical aperture, the fine details of the fields inside the central lobe are not transferred to the imaging plane. To summarize, our experiments show that the onset of the Bessel pulse generates a plasma with a sub-wavelength diameter and that the trailing part of the laser pulse is significantly absorbed.

We determine the typical plasma density profile with a series of numerical simulations with different plasma profiles. We limited the turning radius to r t = 500 nm and chose the plasma transverse profile as a Gaussian distribution for which we adjust peak and width. Collisional PIC simulations for sub-critical plasmas were showing an absorption of only a few percent, even for collision times as short as 0.1 -2.5 fs. As an example, with a peak density of 0.25 n c , the turning radius has to exceed 900 nm to reach an absorption of 20%. However, this would cause a remarkable radial shift of the Bessel beam lobes which is not found in our experiments. In contrast, only simulations with over-critical densities were showing strong absorption in the range of 40-60% as in our experimental results.

The experimental near field profile of Figs. 3(a) and 3(b) is not cylindrically-symmetric. With circular plasma rods, we were not able to reproduce the orientation of the asymmetries, neither the far-field distribution [see Fig. 4(a)]. In contrast, we obtain a very good quantitative agreement with all our experimental results using elliptical plasma rods, having the major axis oriented perpendicular to the polarization (critical radius r c = 75 -190 nm along the polarization direction and r c = 380 nm perpendicular to the polarization).

The ellipticity can be explained by the field amplification in the first stage of field ionization, due to the difference in permittivity between the medium and the initially sub-critical plasma [START_REF] Bhardwaj | Optically produced arrays of planar nanostructures inside fused silica[END_REF][START_REF] Liao | High-fidelity visualization of formation of volume nanogratings in porous glass by femtosecond laser irradiation[END_REF]. We experimentally confirmed that the plasma is elliptical and elongated perpendicular to the polarization, by high-resolution imaging of voids formed in sapphire after the laser-induced micro-explosion, as shown for different input polarizations directions in Fig. 3(e).

In Figs. 3(f)-3(i), our simulations of the near field show negligible lobe shift of the Bessel beam and the asymmetries of the fluence distribution are oriented as in the experiment (we remind that the small dip observed in the central lobe of Figs. 3(h-i) is filtered by the imaging operation). In the collisional plasma model [Fig. 3(g) solid line], the pulse energy decreases linearly with a slope of -0.03 µJ/µm and the total absorption is 54%, both in good agreement with the experimental values. Overall, a steep plasma profile tends to increase the absorption factor and a narrow plasma density profile reduces the shift due to wave-turning. Importantly, the dashed curve in Fig. 3(g) shows the result for a collisionless simulation. Since the difference with the collisional case is only a few percent (5 points), the main absorption mechanism is collisionless resonance absorption.

Our simulations show that the plasma diameter and its cross-section geometry strongly affect the far-field pattern. In the linear, absorption-free, regime, the far-field fluence of a Bessel beam is a homogeneous ring [Fig. Overall, our simulations allowed us, up to here, to identify that the plasma is over-critical and with an elliptic cross-section.

We experimentally observed second harmonic emission from the bulk of sapphire despite its zero secondorder nonlinear susceptibility [START_REF] Boyd | Nonlinear Optics[END_REF]. For this, we imaged the far-field fluence distribution in the spectral range 400±20 nm, as shown in Supplementary Fig.

S.1(c). Our experimental technique is described in the Supplemental

Material [18]. The distribution is composed of a lowintensity background originating from black-body radiation, and of a thin second harmonic emission at an angle nearly identical to the reflection of the pump. This reflection is superimposed to the transmission of the pump because of the conical interaction. We show in Fig. 4(b) that our PIC simulations are in very good agreement with the experimental results.

In laser-plasma interaction, second-harmonic emission originates either from resonance absorption or from parametric decay instability [START_REF] Erokhin | Second harmonic generation by an electromagnetic wave incident on inhomogeneous plasma[END_REF]. In the latter case, the second harmonic polarization is perpendicular to the incident laser one [START_REF] Vlnogradovand | Secondharmonic generation in an inhomogeneous laser plasma[END_REF] while in the former case, it is parallel [START_REF] Auer | Second-harmonic emission at resonance absorption[END_REF][START_REF] Dragila | Second-harmonic generation in a laserproduced plasma[END_REF], as our experimental results. Therefore, the second-harmonic diagnostic confirms that resonance absorption occurs.

In the simulations, the ratio of second harmonic to the fundamental intensity is ∼ 10 -5 . Using this ratio for Fig. S.1(c) and Stefan-Boltzmann law, one can estimate the plasma temperature on the order of 10 eV. This is consistent with our numerical framework and with the fact that Bessel beam-induced plasma relaxation forms warm dense matter in silicon dioxide [START_REF] Del Hoyo | Nanoscale confinement of energy deposition in glass by double ultrafast Bessel pulses[END_REF].

We have demonstrated, for the first time to our knowledge, i) that ultrafast Bessel beams can generate overcritical plasma within the bulk of sapphire, ii) that collisionless resonance absorption is a key process for energy deposition and iii) second harmonic emission in single shot from the bulk of sapphire. Our findings therefore open a new route to generate high energy density matter inside solids. They answer a central question in the energy deposition by ultrafast pulses within the bulk of solids, which is particularly crucial in the field of laser micro-/nano-structuring of materials. Since the conical shape is propagation-invariant, our results can be easily extended to much longer propagation distances: a pulse energy of 1 mJ is enough to create a 1 cm long plasma in identical conditions as discussed above [START_REF] Meyer | Extremely high-aspectratio ultrafast Bessel beam generation and stealth dicing of multi-millimeter thick glass[END_REF].

Nanoplasma generation with over-critical density inside solids opens interesting opportunities for nonlinear plasmonics [START_REF] Kauranen | Nonlinear plasmonics[END_REF], strong THz fields generation [START_REF] Kampfrath | Resonant and nonresonant control over matter and light by intense terahertz transients[END_REF] and extreme ultraviolet sources [START_REF] Han | High-harmonic generation by field enhanced femtosecond pulses in metal-sapphire nanostructure[END_REF]. Controlling resonance absorption inside dielectrics provides useful new tools to drive solids into extreme thermodynamics pathways in a geometry where the material cannot expand into vacuum. The energy density deposited in our experiments is on the order of MJ/cm 3 , which is a typical range for driving a transformation to warm dense matter [START_REF] Denoeud | Metallization of warm dense SiO 2 studied by XANES spectroscopy[END_REF][START_REF] Ernstorfer | The formation of warm dense matter: Experimental evidence for electronic bond hardening in gold[END_REF]. Consequently, millijoule energies are enough to generate relatively large volumes of warm dense matter on the order of 1000 µm 3 .

Our results therefore provide new avenues for generating relatively large volumes of new material phases and our configuration can be considered as a convenient new platform for the exploration of warm dense matter physics.

K.A and R.M equally contributed, with the largest fraction of, respectively, simulation work and experimental work. Technical assistance by C. Billet and E. Dordor as well as fruitful discussions with J.M. Dudley and D. Brunner are gratefully acknowledged. We thank the EPOCH support team for help (https://cfsapmw.warwick.ac.uk), and French RENATECH network.

The authors acknowledge the financial supports of: European Research Council (ERC) 682032-PULSAR, Region Bourgogne-Franche-Comte and Agence Nationale de la Recherche (EQUIPEX+ SMARTLIGHT platform ANR-21-ESRE-0040), Labex ACTION ANR-11-LABX-0001-01, I-SITE BFC project (contract ANR-15-IDEX-0003), and the EIPHI Graduate School ANR-17-EURE-0002. This work was granted access to the PRACE HPC resources at CINECA, Italy, under the Project "PULSARPIC" (PRA19 4980), PRACE HPC resource at TGCC, France under the Project "PULSARPIC" (RA5614), HPC resource at TGCC, France under the projects A0070511001 and A0090511001, and Mésocentre de Calcul de Franche-Comté.

Our numerical simulations model a plasma of electrons and ions in vacuum. We used ion-to-electron mass ratio 102 × 1836 as the product of the sapphire molar mass and the proton mass. We injected from the z = 0 boundary a Gaussian pulse which propagates along the positive z-direction and is polarized along the x-direction. We applied a phase Φ(r) = -(2π/λ)r sin θ to the Gaussian beam, as it is the case experimentally using the spatial light modulator. The wavelength and cone angle are λ = 0.8 µm, 25 • , respectively. The temporal profile of the beam is a Gaussian function with a width of 100 fs FWHM. The Gaussian beam waist is w = 10 µm. All simulations using a reduced cone angle, to simulate refraction, gave very similar results in terms of absorption, characteristics of near and far-field patterns. The Bessel beam length has been reduced to ≈ 18 µm, by cropping the Gaussian beam window, to reduce the simulation run time. The peak intensity in the Bessel zone is 6 × 10 14 W/cm 2 in absence of plasma, i.e., on the same order of magnitude as in the experiments.

Plasma parameters

We have used circular and elliptical plasma rods. The axial density profile of the plasma rod follows tanh(z/z 0 ) with z 0 = 1 µm. It shows a z-invariant density profile extending from ≈ 2 µm away from the onset of the Bessel beam. The velocity distribution of both plasma species have been initialized with a Maxwellian distribution at T e = T i . We have run simulations for different initial plasma temperatures of 1×10 -3 , 1 and 10 eV and we have obtained very similar results in terms of pulse absorption, structure of the fields, and hot electron population. All simulations results have included electron-ion collisions, although the collisionless case is almost indistinguishable.

Resolution

We have used a computational box of 15 × 15 × 30 µm 3 volume and run the simulations up to t run = 320 fs. The spatial resolution of the grid for second-order FDTD is set so that dxk 0 r = dyk 0 r = 0.04, and dzk 0 z = 0.1 where k 0 r = k 0 sin θ, k 0 z = k 0 cos θ. Using a fourth-order FDTD solver has not shown any significant change of the results. The temporal resolution is constrained by the Courant stability condition. We have used the convolutional perfectly matched layers boundary condition for the fields and open boundary condition for the particles. After testing the simulations with different numbers of particles per cell from 32 to 128 to ensure energy conservation, we have chosen 32 particles per cell per species (a total number of 550 million particles). We have used a first-order triangle shape function with 3 points to represent particles giving third-order particle weighting into the grid. We have obtained similar results using a third-order b-spline particle shape with 5 points. In the simulation of laser-plasma interaction using PIC simulation, the Debye length with typical value in the range 0.2 -2 nm is not resolved by the grid cell, as it is the case in most simulations of laser-solid interaction [START_REF] Arber | Contemporary particle-in-cell approach to laser-plasma modelling[END_REF]. However, the energy is conserved using the energy conservative scheme for the integration of particle trajectory. In the EPOCH PIC code, the numerical heating is reported to grow as dT eV /dt ps = α H n 3/2 23 ∆x 2 nm /n ppc where T eV is the temperature in eV, t ps time in ps, n 23 density in 10 23 1/cm 3 , ∆x nm grid cell in nm, n ppc number of particles per cell, and α H depends on the particle shape and current smoothing. For the triangular particle shape with current smoothing and the above resolutions α H = 60. Therefore, for the chosen resolution dT eV /dt ∼ 1 eV/ps.

Far-field distributions for first and second harmonics

We have obtained the intensity spectrum I(ω, k x , k y ) by performing a discrete Fourier transform on B x:y:z (t, x, y) at a fixed propagation distance of z = 20 µm. The Fourier transformation has been performed on the recorded data for |x| ⩽ 5 µm and |y| ⩽ 5 µm. This is the reason for the width of the simulation far-fields in Figs. (S.1). The first and second harmonic radiation spectra are then obtained by filtering the power spectrum at the central frequency of the pulse ω 0 , and 2ω 0 , respectively.

EXPERIMENTAL SETUP Fluence distributions

We spatially shaped 100 fs laser pulses at a central wavelength of 800 nm. Using a spatial light modulator combined to a 2f-2f telecentric arrangement to produce a Bessel beam with cone angle 25 • in air. The pulse duration of 100 fs has been characterized at the sample position. After the interaction, the pulse is collected with a ×100 microscope objective (Olympus MPLFLN) in a 2f-2f arrangement to image the pulse on a camera (Stingray F146B, 14 bits). The imaging system, with a numerical aperture of 0.9 is placed on an independent S.2 translation stage. The near-field fluence distributions of Fig. (3) have been obtained by interrupting the propagation of the Bessel beam in the sample at the exit surface, as described in detail in reference [START_REF] Xie | Tubular filamentation for laser material processing[END_REF]. The evolution of energy along the propagation direction has been measured by spatially integrating on the camera the far-field fluence at each propagation distance. The overall absorption in the sample has been confirmed by measuring the pulse energy on large-area photodiodes before and after the sample, as in reference [START_REF] Del Hoyo | Nanoscale confinement of energy deposition in glass by double ultrafast Bessel pulses[END_REF].

Imaging of second harmonic generation

Far-field images were recorded on a camera using an accumulation over 500 shots when the sample is continuously translated to separate the laser impacts by 5 µm. The field was collected using a ×50 microscope objective (Olympus MPLFLN). The far-field distributions of

  ld En er gy de po sit ion ou t of th e ini tia l vo lum e Ov er -cr itic al pla sm a de ns ity Un de r-c riti ca l pla sm a de ns ity Wave conversion: resonance absorption Wave turning Critical surface En er gy de po sit ion ins ide th e ini tia l vo lum e

FIG. 2 .

 2 FIG. 2. Near-field fluence distribution of the Bessel beam from PIC simulations. Fluence distribution in xy-plane at z = 7 µm (peak of the axial fluence profile), (a) in the absence of plasma and (b) in the presence of a circular plasma rod with a transverse Gaussian density profile. (c) Zoom-in view of the central part of (b).

  ) and3(b) show the xy-cuts of the distribution at the peak of the axial profile (z = 20 µm).

  Figure 3(c) shows the fluence distribution in zx-plane while Fig. 3(d) displays the evolution of the pulse energy as a function of propagation distance, measured with the imaging technique.

FIG. 3 .

 3 FIG. 3. Near-field fluence distributions in sapphire: experiments (left) and PIC simulation (right). (a) and (h) Slices in xy-plane at z = 20 µm in (a) and z = 7 µm in (h). (b) and (i) Zoom-in views of (a), (h) respectively. (c) and (f) Slices of the fluence in the zx-plane (y = 0). (d) and (g) Evolution of pulse energy as a function of propagation distance z for collisional (solid blue line) and collisionless simulation (dashed red line). (e)Scanning electron microscopy images of void channels produced in single shot illumination for different polarizations. The leftmost figure is for circular polarization and the channel cross-section is circular. In all other cases, the polarization is linear, oriented along the white arrow.

  1(b)]. Supplementary Fig. S.1(a) shows the experimental far-field fluence distribution collected after the interaction. Its angular distribution is illustrated in Fig. 4(a) (solid blue). It shows two lobes oriented in the direction of the input pulse polarization. The far-field from the simulation [Fig. 4(a), red dashed line] is in quantitative agreement with our experimental data for the elliptical plasma rod.

  FIG. S.1. Far-field fluence distributions for the first and second harmonic. Far-field distribution for first harmonic from (a) experiment and (b) numerical simulation using the same parameters as in Fig. 3. (c) Experimental far-field distribution of the emission in the spectral range 400 ± 20 nm and (d) simulated far-field distribution for the second harmonic. All axes are normalized by the radial component of the Bessel pulse, k 0 r = 2π sin θ/λ.

Supplemental material

PARTICLE-IN-CELL SIMULATIONS

Pulse injection