Maxime Wawrzyniak
email: maxime.wawrzyniak@grenoble-inp.fr

Julien Bras

Aurore Denneulin

Tân-Phu Vuong

Influence of mesh geometries on the design of transparent antennas at 2.45 GHz

Keywords: Transparent antennas, Meshed antennas, Dipole antennas, Printed Antennas

This paper presents optically transparent dipole antennas with innovative meshes for printing processes. The influence on antenna performance of the meshing geometry, the width and the pitch of dipole are investigated. The study shows that, for a given width, an increase of the performance with a twin small pitch with circle geometry. Furthermore, the antennas with an optical transparency of 70% present a loss of the realized gain around 0.35% compared to an opaque conventional dipole antenna with the same width.

I. INTRODUCTION

Nowadays, antennas and Internet of Things (IoT) present an important part of the economy and lifestyle in the world. The development of transparent antennas is a new challenge to tend new markets, especially in smart packaging or smart building. Besides, the uses of additives processes to produce those types of antennas like screen-printing or ink-jet provide an innovative touch and new conveniences for flexible IoT for example. Indeed, printing processes allow the production of antennas on larger flexible substrates like polyethylene terephthalate (PET), paper by an additive process limiting the amount of product used and the environmental impact. The development of flexible antenna for energy scavenging by 3D printing in [START_REF] Bui | Design and Measurement of 3D Flexible Antenna Diversity for Ambient RF Energy Scavenging in Indoor Scenarios[END_REF] allows tending new markets. The design of antenna using flexible substratepaper-for energy harvesting at 1800MHz describe in [START_REF] Bui | Gain enhancement of suspended miniaturized antenna on high-loss paper substrate[END_REF] shows compact antenna with high gain.

However, one of the notable problems to develop transparent and flexible antennas by printing processes is the ratio conductivity/transparency of the conductive ink. The better is the conductivity, the less the pattern is transparent. A solution to obtain an excellent transparent film with a good conductivity is Indium Tin Oxide (ITO) (Sheet resistance Rs = 5-70 Ω.sq -1 for %T > 85% @550nm). ITO presents several problems which are its fragility and its implementation.

An innovative technique for the development of optically transparent antennas is the meshing method like describe in [START_REF] Bui | Design and Measurement of 3D Flexible Antenna Diversity for Ambient RF Energy Scavenging in Indoor Scenarios[END_REF]. The antennas develop by meshing method have lower performance in terms of realized gain or radiation than their no-mesh homologue. In the case to obtain meshed antennas with a loss of performance as low as possible and the best transparency, the geometry of the meshing is studied here with four different types: honeycomb, square, diamond and circle (Fig. 1b).

An important point with this meshing is the size of the pitch. Indeed, a relation linking the wavelength λ 0 , the size of the pitch and the performance has been developed in [START_REF] Martin | Influence of the mesh dimensions on optically transparent and active antennas at microwaves[END_REF]. Based on the characteristic of an additive printing process, the screen printing, developed in the next section, the study of the antenna design will be discussed. For that, the comparison of the mesh geometries and the pitch inside the mesh will be realized.

II. PRINTING PROCESSES

To develop those antennas, the specifications of an additive printing process must be considered. In this case, the technique of screen printing was chosen. It is a process which can be used on an industrial scale, for its high productivity, its repeatability and it is an additive technique, so environmentally friendly. The screen printing process is described in fig. 2. First, the conductive paste is deposited on a screen with the designed antenna (fig. 2a). The substrate is below the screen. Then, with a squeegee, the paste is transferred on the substrate according the scheme on the screen by a short and thin contact between the screen and the substrate (fig. 2b). It is important to underline that the speed and the tilt of the affect the accuracy of the pattern. At the end, after the passing of the squeegee, the squeegee removes the ink and a new substrate is placed below the screen to start a new printing (fig. 2c).

One of the most important points with the screen printing is the screen itself. It is composed of polyester thread with a given density and diameter. If the density of thread is important, then the quantity of ink passing inside the screen is low and thus the thickness too. The minimal width is given by the diameter of the thread. It is established than the minimal width is equal to three times the diameter of the thread. In the case of this article, the diameter of the thread is around 34 µm; the minimal width w is 100 µm. The distance between the substrate and the screen, the off-contact, is important too. If the off contact is too important, the scheme will not be printed on the substrate. If it is too short, the resolution of the pattern will be affected.

To design and simulate according to those specifications, the sheet resistance of a conventional conducive ink is used for the simulations, presenting a sheet resistance R s = 30 mΩ.sq -1 . The substrate used is a PET Melinex ST726 from Dupont-Teijin (thickness: 175 µm, ε r : 2.88 @ 2.45 GHz, tan δ: 0.024 @ 2.45GHz).

III. ANTENNA DESIGN

The antennas presented previously were designed using commercial software, CST Studio Suite. The choice of the geometry is motivated by the originality of the mesh. The feasibility of meshes square antennas was studied in [START_REF] Kang | Transparent Patch Antenna Using Metal Mesh[END_REF]. The meshing in honeycomb has been developed to improve communications inside buildings in [START_REF] Gustafsson | Design of frequency selective windows for improved indoor outdoor communication[END_REF]. The geometry tends to improve the bandwidth and the stability of the patch. The benefit of diamond meshing obtained by sputtering was studied in [START_REF] Lee | Electrical Characterization of Highly Efficient, Optically Transparent Nanometers-thick Unit cells for Antenna-on-Display Applications[END_REF]. The design allows an optical transparency for an equal sheet resistance compared to an opaque antenna. However, according to our research, there are no studies about meshes dipole antennas with circle or honeycomb geometry. The impact of the pitch was evaluated in [START_REF] Martin | Influence of the mesh dimensions on optically transparent and active antennas at microwaves[END_REF]. Furthermore, the performance and the optical transparency of the antenna are linked to the wavelength λ 0 and the pitch following [START_REF] Bui | Design and Measurement of 3D Flexible Antenna Diversity for Ambient RF Energy Scavenging in Indoor Scenarios[END_REF].

𝜆 0 𝑝 = 𝑥 (1)
The factor 𝑥 must be close to 100 for a good ratio transparency/performance. A value below 100 will conduct to a very transparent antenna but underperforming. On the contrary, a value upward corresponds to an antenna with a high performance for a low transparency. In light of this, knowing the wavelength λ 0 for our application, the pitch p and the strip width s is defined.

The dimensions are given in Table 1. The optical transparency in the light visible spectrum has been calculated from [START_REF] Bui | Gain enhancement of suspended miniaturized antenna on high-loss paper substrate[END_REF]:

𝑇(%) = [(𝑝 -𝑠)/𝑝]². 𝑇 𝑠𝑢𝑏 ( 2
)
T sub is the optical transparency of the substrate used (0.87 or 87%). The strip width s is the same for all antennas due to the printing processes. The value of the pitch changes according to the antennas. They are composed of a single or a twin line of meshes. The transparency is affected, from 69.65 for a single line with a total width w/2 to 78.91 % for a single line of width w. The ratio 𝑥 is increased slightly to 128.89 from 58.31. The first value is closer to 100, the ideal ratio for optical transparency and performance. Hence, the antenna type 1 with a width of w/2 should present the best compromise between performance and transparency. Moreover, two squares were designed to realize an easier connection with devices easier and they are included in all following simulations. The aim of the study is to develop new type of mesh dipole antenna, produced by a printing process and optically transparent for application at the 2.45 GHz frequency. The design of those antennas was realized previously.

Based on those requirements, the realized gain is compared to the optical transparency of the antennas to investigate the influence of several geometries meshes. For this purpose, antennas were adapted by playing on the distance between each part of the antenna.

A. Reflection Coefficient |S 11 |

The |S 11 | parameter is simulated for each antenna. First, the |S 11 | for a pitch of 2.1 mm and a total width of 2.3 mm is presented in fig. 3. The antennas were optimized and adapted. The adaptation is better for meshed antennas than the reference opaque antenna. It can be explained by the meshed geometry. Each geometry acts like a small resonator, increasing the signal of the antenna. Secondly, the |S 11 | for a pitch of 1.9 mm and a total width of 2.3 mm is presented in fig. 4. The adaptation at 2.45 GHz is realized and every meshed antenna presented a better signal than an opaque reference antenna. The value of |S 11 | coefficient is lower than in fig. 3, from -24.96 dB for the square in fig. 3 to -20.86 dB for the same geometry in fig. 4. In general, a decrease of around 10% of intensity is observed. Those antennas were designed with a double line of meshes with the same pitch p. The proximity between those lines leads to an interference between each meshes, limiting the coefficient reflection. Third, the antenna with a single line of meshing for a pitch p of 0.95 mm and a total width w/2 of 1.15 mm is investigated in fig. 5. The adaptation of those antennas was realized and a decrease of the reflection coefficient is noted. This decrease of the intensity is expected because of the decrease of the pitch, limiting the resonating effect. However, the intensity stays correct with a signal |S 11 |< -16 dB. The decrease of the peak intensity is around 6%, which is acceptable for a decrease by 2 of the size.

B. Realized Gain

The design of each antenna was adapted for the frequency f 2.45 GHz. The realized gain of those antennas is studied in this part. The results are presented in Table 2. The realized gain by those antennas will strongly depend on the size of the pitch p and the width w.

For antennas with a pitch p = 0.95 mm and width w = 1.15 mm, the ratio 𝑥 is 128.89 (see Table 1). The mesh antenna with the best gain is the circle followed by the honeycomb, the square and the diamond. The value observed for the realized gain confirms this model, with a realized gain between 1.85 dBi for the diamond geometry and 1.949 dBi for the circle geometry. The difference is very small, around 5%, and only 1% with an opaque reference antenna. On the contrary, the gain in optical transparency is important, from 0% to 69.65%.

For antennas with a pitch p = 0.95 mm and a width w = 2.3 mm, the best mesh antenna is the circle, followed by the honeycomb, the diamond and the square. The realized gain here is between 2.005 dBi for the circle and 1.951 dBi for the square, a loss of gain about 2.69 %. The difference with a reference antenna is between 2.57 % for the circle and 5.2 % for the square, with an optical transparency from 0% for an opaque to 78.08% for those models.

To conclude, antennas designed with a pitch p = 2.1 mm and a total width w = 2.3 mm are investigated. The realized gain changes the order of antennas. The honeycomb is the best mesh antenna with 1.906 dBi, followed by the square, 1.879 dBi, the circle, 1.87 dBi and the diamond with 1.808 dBi. Those values present a higher variation than before, with amplitude of 5.15 % between them and up to 12.15 % compared to the reference antenna. The variation in the list of best meshing can be explained by the ratio between the low contact among geometries and their high surface for meshed circle and diamond antenna.

Indeed, honeycomb and square present line in contact inside the structure, allowing a better diffusivity of the radiation in the field. The low contact between circles or diamonds creates important loss of current, thus loss of radiation. This case is in agreement with the ratio 𝑥 calculated in Table 1, 58.31. That value is synonym of low performance but high transparency for those antennas, which is the case with an optical transparency of 78.91%.

The relation between optical transparency and realized gain shows that the difference of optical transparency between the antennas type 2 and 3 is very low, 0.83% but the loss of performance is more important. The difference between the type 1 and 2 is the optical transparency, with a smaller dispersion in terms of realized gain with the type 2 than the type 1 for the same pitch. This can be attributed to the twin line of each pattern, increasing the radiation in the field better than a single line. V. CONCLUSION The design and the study of optically transparent meshing antennas were realized. The pitch p, the width w and the geometry were studied. Those antennas were designed to be manufactured by printing processes like screen printing on flexible substrate for IoT applications at 2.45 GHz. The adaptation of those antennas were investigated, showing an influence of the geometry and the width on the |S 11 | parameter, with a decrease from -24.96 dBi for a meshed square antenna with a width w = 2.3 mm to -19.71 dBi for a meshed square antenna with a width w = 1.15 mm. The pitch p influences greatly the optical transparency of the antenna. Lower is the pitch, lower is the optical transparency. However, lower is the pitch, better is the performance. A compromise must to be found to conserve high performance and high optical transparency. For that, the idea is to design antennas with medium pitch in twin line like antennas type 2, allowing a high transparency, 78.08% with a realized gain near an opaque and traditional antenna, 2.005 dBi for a meshed twin-circle antenna and 2.058 dBi for an opaque antenna. Honeycomb meshing is interesting for small antennas, presenting the geometry with the smallest difference whatever the geometry or the pitch used. For small antennas, with a width w = 1.15 mm, the best antennas are those with a high contact in the meshing. The following step is to produce and confront theoretical results to practical results.

Fig. 1 :

 1 Fig. 1:( a) Geometry of a mesh square dipole antenna with a pitch p and a width w. (b) Design of dipole antenna with different width w and mesh geometry: honeycomb, square, circle and diamond. On the left, the first type for w/2. On the right, the second type for w.

Fig. 2 :

 2 Fig. 2 : Scheme of the screen printing. (a): before printing. (b): printing. (c): after printing

Fig. 3 :

 3 Fig. 3: Reflection parameter |S11| for meshed antenna with a pitch p of 2.1 mm and a total width w of 2.3 mm. In the insert, zoom of the coefficient at 2.45GHz.

Fig. 4 :

 4 Fig.4: Reflection parameter |S11| for meshed antenna with a pitch p of 1.9 mm and a total width w of 2.3 mm. In the insert, zoom of the coefficient at 2.45GHz.

Fig. 5 :

 5 Fig. 5: Reflection parameter |S11| for meshed antenna with a pitch p of 0.95 mm and a total width w of 1.15 mm. In the insert, zoom of the coefficient at 2.45GHz.

Table 1 .

 1 Mesh dimensions and transparency associated.

		Meshing
		Antenna	Antenna	Antenna
		type 1 (w/2)	type 2 (w)	type 3 (w)
	Pitch p (mm)	0.95	1.9	2.1
	Strip width s (mm)	0.1	0.1	0.1
	Total width w (mm) 1.15	2.3	2.3
	Optical Transparency T (%)	69.65	78.08	78.91
	Ratio 𝑥	128.89	64.45	58.31
	IV. SIMULATION AND RESULTS

Table 2 :

 2 Realized Gain in dBi for meshes antennas dependant of the pitch p, the width w and the geometry

	Geometry	Pitch p (mm)	Width w (mm)	Realized Gain (dBi)
	Reference 1	0	1.15	1.970
	Circle 1	0.95	1.15	1.949
	Diamond 1	0.95	1.15	1.850
	Honeycomb 1 0.95	1.15	1.898
	Square 1	0.95	1.15	1.853
	Reference 2	0	2.3	2.058
	Circle 2	0.95	2.3	2.005
	Diamond 2	0.95	2.3	1.972
	Honeycomb 2 0.95	2.3	1.992
	Square 2	0.95	2.3	1.951
	Reference 3	0	2.3	2.058
	Circle 3	2.1	2.3	1.870
	Diamond 3	2.1	2.3	1.808
	Honeycomb 3 2.1	2.3	1.906
	Square 3	2.1	2.3	1.879

ACKNOWLEDGMENT

The authors wish to acknowledge University Grenoble Alpes for the financial support with the program "IRS IDEX", the region Auvergne-Rhône Alpes with the project SCUSI and the World Bank FIRST project under the grant number 23/FIRST/1.a/HUST. This research was made possible thanks to the facilities of the TekLiCell platform funded by the Région Rhône-Alpes.


Behrang Moradi
email: behrang.moradi@mines-ales.fr

Nicolas Daclin
email: nicolas.daclin@mines-ales.fr

Vincent Chapurlat
email: vincent.chapurlat@mines-ales.fr

Formalization and Evaluation of Non-functional Requirements: Application to Resilience

Keywords: System of systems engineering, Resilience, Non-functional property, "-ilities"

This paper introduces the development of a method for the specification, formalization and evaluation of resilience. The developed method is based on two working approaches. First, we study and analyze several resilience metrics and indicators as well as the relationship between resilience and other non-functional requirements namely "-ilities". Concepts for evaluation are identified and defined. Further, we map out these "-ilities" by positioning them according to the dynamic of the resilience represented as a set of zones. A set of indicators to evaluate the resilience and particularly indicators that are associated with these "-ilities" to each zone of the resilience has to be selected. The expected benefit of such method is to allow to evaluate resilience in order to master and improve it.

Introduction

To fulfil its mission adequately, a collaborative system must satisfy functional and non-functional requirements. Among the non-functional requirements a set is called "ilities" [START_REF]Advanced automation technologies and their applications -Part 1 : Framework for enterprise interoperability[END_REF] and represents "the desired properties of systems, […] that often manifest themselves after a system has been put to its initial use" [START_REF] De Weck | Investigating Relationships and Semantic Sets amongst System Lifecycle Properties ( Ilities )[END_REF]. For instance, let's mention the Flexibility, Robustness, Safety, Interoperability or Survivability. Figure 1 presents the network of "-ilities" correlations and their relationships as defined in [START_REF] De Weck | Investigating Relationships and Semantic Sets amongst System Lifecycle Properties ( Ilities )[END_REF]. The work proposed attempts to study and analyze "-ilities" as a whole rather than to study an "-ility" in isolation and focuses on the resilience assessment. Resilience is an important property because it must be mastered and maximized [START_REF] Chin | [END_REF] to effectively cope with disruptive events and maintain acceptable levels of services and performance (e.g. loss of an organization in a collaborative network, fire requiring the engagement and collaboration of different organization…). There exist several definitions of resilience. Generally speaking, it is defined as "the ability of the system to resist, absorb, recover or adapt to disturbances and diminish the consequences as well as to recover quickly and effectively" [START_REF] Haimes | On the Definition of Resilience in Systems[END_REF]. Lastly, resilience is practiced in various application area e.g., critical infrastructure monitoring, security, transport [START_REF] Francis | A metric and frameworks for resilience analysis of engineered and infrastructure systems[END_REF], [START_REF] Iii | National Infrastructure Advisory Council A Framework for Establishing Critical Infrastructure Resilience Goals Final Report and Recommendations by the Council[END_REF], [START_REF] Andrews | Fault Modelling in System-of-Systems Contracts[END_REF].

Fig. 1. Correlation network of "-ilities" [2]

The research question deals with the evaluation of the resilience. The prevention, preparation and management of negative perturbations for the security and protection of systems have become a major concern. Indeed, a disturbance may lead to heavy loss of performance and affect a system, so that the evaluation resilience can participate to the improvement of a performance of a system. The purpose is to study the resilience with the consideration of its ecosystem that means including the possible relationships with other non-functional requirements. Currently, resilience is evaluated without considering possible impacts coming from other requirements but also possible impacts generated by resilience as well. As a consequence, the targeted objective is to develop a metric to evaluate resilience numerically and sufficiently generic to be practicable to any networked system subject to any type of disruption. The paper is structured as follows. After this brief introduction, the concept of resilience is presented as well as different methods to evaluate it. The next section presents the concepts which act as foundation for the development of our approach to analyze and evaluate resilience. The final section presents the conclusion and the future perspective for this research.

Resilience Definition and Evaluation 2.1 Definition

There are numerous definitions of resilience. Let's mention the following ones:

-"the intrinsic ability of a system to adjust its functioning prior to, during, or following changes and disturbances, so that it can sustain required operations under both expected and unexpected conditions" [START_REF] Hollnagel | Resilience engineering in practice: A guidebook[END_REF]; -"the ability to anticipate, prepare for, respond to, adapt to disruptions and to mitigate the consequences as well as to recover in timely and efficient manner including preservation restoration of services" [START_REF] Cutter | Disaster Resilience: A National Imperative[END_REF]; They all suggest that resilient systems are able to manage disastrous situation due to several capacities requested throughout the classical phases of the disaster management lifecycle: Anticipation (Preparation, Prevention), Response (Absorption, Adaptation) and Recovery (Figure 2).

Fig. 2. The classical resilience dynamic

Anticipation (Prevention and Preparedness) aims at identifying and minimizing the risks of the occurrence of an event. This zone concerns also the preparation to face up an event [START_REF]Disaster Planning: prevention, response, recovery[END_REF]. Response (Absorption and Adaptation) expresses the absorptive capability (robustness), i.e., the ability to reduce the negative impacts caused by disruptive events and minimize consequences with less efforts [START_REF] Chin | [END_REF], [START_REF] Haimes | On the Definition of Resilience in Systems[END_REF]. The adaptive capability (adaptability) refers to the ability to adapt to disruptive events through self-organization (flexibility, interoperability) to minimize consequences and it can be enhanced by using emergency systems. Recovery is defined as a return to a qualified acceptable condition. The restorative capability refers to the ability of the system to rapidly be repaired (maintainability, repairability) and return to a, as much as possible, normal and a reliable functioning mode that meets the requirements for an acceptable and desirable level of quality of service and expected control [START_REF] Chin | [END_REF].

The study and synthesis of different definitions shows that the authors believe resilience is characterized by zones such as Anticipation, Recovery and Response; each author considers more or less zones in their study (e.g. for [START_REF] Nogal | Resilience of traffic networks: From perturbation to recovery via a dynamic restricted equilibrium model[END_REF] resilience is a problem of response and recovery) (Figure 3). As part of resilience assessment, we consider the three areas of dynamic of resilience, as defined by [START_REF] Cox | Transportation security and the role of resilience: A foundation for operational metrics[END_REF].

Fig. 3. Resilience dynamic

Resilience Metric

Resilience can be assessed in different ways. It can be evaluated by measuring the performance or loss of performance of a system before and after the disruptive event, the potential loss of functionality, the loss of quality of service, the effectiveness of the security barriers, as well as the activities recovery. Numerous works related to the evaluation of the resilience are provided in the literature e.g. [START_REF] Henry | Generic metrics and quantitative approaches for system resilience as a function of time[END_REF] [15] [START_REF] Francis | A metric and frameworks for resilience analysis of engineered and infrastructure systems[END_REF] and [START_REF] Zobel | Comparative Visualization of Predicted Disaster Resilience[END_REF] that evaluates resilience with different points of view. [START_REF] Henry | Generic metrics and quantitative approaches for system resilience as a function of time[END_REF] proposes a metric of resilience that can be associated in two types such as the focus attribute parameters, which usually consist of indices based on subjective assessments and the indicators built on databases, which quantify the system attributes that contribute to resilience. The performance-based methods, which measure the consequences of system disturbances and the impact that system attributes have on mitigating these consequences. [START_REF] Francis | A metric and frameworks for resilience analysis of engineered and infrastructure systems[END_REF] states the measurement of resilience is a function of the 3 capacities (absorption, adaptation and recovery) as well as recovery time, through the measurement of the performance and its evolution. The method is based on a resilience analysis framework and a metric for measuring resilience. The analysis framework consists of system identification, resilience objective setting, vulnerability analysis, and stakeholder engagement. Lastly, [START_REF] Zobel | Comparative Visualization of Predicted Disaster Resilience[END_REF] provides a quantitative measure of resilience in the face of multiple disaster-related events. It extends the concepts of the resilience triangle and predictive resilience in disaster by considering the trade-offs between several criteria. Its work is based on sudden disasters and the initial impact of each event as well as the recovery time of the system before the next event. In this work (Figure 4), robustness is used to increase the resilience so that it recovers its performance and returns to an acceptable state. Thus, there is a link between resilience and robustness. These works show three approaches to assess resilience (Figure 5). Let's note that [START_REF] Zobel | Comparative Visualization of Predicted Disaster Resilience[END_REF] highlights the link between resilience and another "-ility" (robustness in the Zone2-response). Its measurement shows the importance of considering the link between "-ilities" since the more the robustness, the more the resilience can be efficient. However, each metric treats the resilience in isolation, i.e., they do not consider the possible relationship with other "-ilities". In this sense, stakeholders don't have any information about the possible impact of the resilience onto other "ilities" and vice versa. Thus, the ecosystem of "-ilities" and their relationship can be used and study to evaluate a given "-ility", here, the resilience.

Research Work Proposal

The assessment of resilience relies on defining and analyzing the set of "-ilities", i.e., the analysis and formalization of the relationship between resilience and other "ilities" (Figure 6). In this hypothesis, we focus on the analysis of the resilience and its environment and highlight the various components to consider to evaluate resilience. The four components considered are (in red and numbered on Figure 6): 1. The influence. It identifies which "-ilities" influence resilience. Some influences are currently identified. However, as claimed in [START_REF] De Weck | Investigating Relationships and Semantic Sets amongst System Lifecycle Properties ( Ilities )[END_REF], some might exist but are not yet identified. In order to assess resilience based on all elements, it is necessary to identify any dependence between resilience and other "-ilities".

The orientation.

It means to define if the influence is unidirectional (ex. quality → resilience) or bidirectional (ex. quality ↔ resilience). This orientation must be considered "from" resilience "to" another "-ilities" as well as "from" another "ilities" to resilience.

Dependence. It defines the intensity of the variation between two "-ilities".

For instance a high variation (positive or negative) of an "-ility" leading to a high variation (positive or negative) of the impacted "-ility" expresses a high dependence. 4. The propagation. The chain represents a relation "starting from" the resilience and returning to the resilience via another "-ilities" (resilience → safety → sustainability). In this work we consider and limit a chain to a path with 3 "-ilities". In this hypothesis, we present the "-ilities" that have links with the resilience and thus we analyze their relations based on the four components (influence, orientation, dependence, and propagation). Figure 7 shows the set of "-ilities" in relation with the resilience. Some links stem from [START_REF] De Weck | Investigating Relationships and Semantic Sets amongst System Lifecycle Properties ( Ilities )[END_REF], and some are added following the study of the "ilities" and their possible relationships. For instance, interoperability is linked with resilience, since it enables a collaborative system to collaborate coherently to achieve the desired operational effect, so the relationship with resilience -e.g. to mitigate crisis situation -is needed and important. Adaptability is an "-ility" expected in the dynamic of resilience (response zone -ability to adapt), so it has a direct link to resilience, which helps to minimize a negative impact. Then a given link must be characterized by the four components defining a relation. For instance, the sustainability influences (component 1 -influence) the resilience that means a variation of sustainability leads a variation of the resilience. Then, the direction (component 2 -orientation) of this influence is directed from sustainability to resilience, because sustainability allows the system to withstand shocks (Zone 2 -response). The force (component 3 -dependence) is defined such as the high increase of sustainability leads to a high increase of the resilience. Lastly, the propagation (component 4 -propagation) represents the chain -limited to three path -starting from the sustainability via the resilience. In this example the chain is characterized by the path sustainability -resilience -safety (with a last feedback to sustainability). Figure 8 summarizes the relation between resilience and sustainability in agreements with the four items of the first hypothesis. In this end, each relationship between resilience and other "-ilities" (which impact resilience) have to be identified and formalized. In the same way, the components, such as dependence and propagation, must formally established to allow the evaluation of the resilience (e.g. quantification or qualification of dependence and definition of effect in the propagation chain).

Fig. 7. Network of correlation of "-ilities" and resilience

Based on these first components presented, we will define resilience indicator that will measure and manage the capacity of a collaborative system to recover from an event. The indicator considers the capacity to cope with the consequences of disturbances. In addition, the indicator explains the impact of anticipation, response and recovery activities that could be taken after the disruption to reach the acceptable level of service (performance).

Fig. 8. Characterization of the relation between resilience and sustainability

Moreover, the resilience dynamic must be considered. Indeed, the aim is to know the level of resilience for each zone to implement adapted solution to improve resilience. To this purpose, "-ilities" and their influences are mapped in each zone (e.g. flexibility can be expected during the prevention, Figure .9). This positioning is relative to the analysis of resilience and "-ilities" that have identified links in each area. The objective is to get a resilience indicator for each zone. In the end, the aggregation of each indicator will provide an evaluation of the resilience. Thus, each "-ilities" related to resilience is analyzed to be re-located precisely on the corresponding phase of resilience. This analysis is mainly related to the study of the intrinsic characteristics and their understanding of a given "-ility" with regards to characteristics expected during a given phase of the resilience. It is to note that a given "-ility" can cover several phases of resilience life-cycle. For instance, robustness is interpreted as a measure of performance change. It is positioned in anticipation zone, because the effect of robustness allows the system to increase the readiness to deal with disruptive events. It is also positioned in the response zone, which makes it possible to absorb the negative effects of a disturbing event and increase the level of resilience of the system. Adaptability is the ability of a system to change to perform its basic work in uncertain or changing environments. Thus, adaptability is positioned in the response zone (figure 9), by minimizing the negative impact by protection against shocks. As last example, flexibility can be defined as the ability of a system to comply with its core mission that is not included in the definition of system requirements in disrupted or changing environments. This can be conceptualized as minimizing the consequences with less effort [START_REF] Bordoloi | Flexibility, adaptability, and efficiency in manufacturing systems[END_REF]. Thus, the flexibility is positioned on response and recovery zones. Figure 9 shows the mapping of the "-ilities" with the different resilience zones (e.g. flexibility is positioned in zone 2, zone 3 and robustness in zone 1, zone 2, zone 3). Mapping makes possible to establish the resilience indicators associated with these "-ilities" and for each zone. These indicators ultimately enable the level of resilience to be accurately identified and assessed, so aggregation of all these indicators will provide an assessment of the overall resilience.

Conclusion

The here presented work aims, in the end, to evaluate the resilience relying on the dynamic of the resilience and on its study as an "-ilities" belonging to an ecosystem of "-ilities". The purpose is to support a collective of actors -for instance involved in a collaborative network -to manage their resilience based on the knowledge of its level and to improve it. First, several resilience metrics are studied and analyzed as well as the relationship between resilience and other "-ilities". Then, the components that defines the relationship between "-ilities" are defined and "-ilities" linked to the resilience are mapped by positioning them according to its dynamic. Future work is related to the formalization of the components of relationship to get metric and to evaluate the resilience.

Fig. 4 .

 4 Fig.4. The predicted resilience triangle as a proportion of T*[START_REF] Zobel | Comparative Visualization of Predicted Disaster Resilience[END_REF]

Fig. 5 .

 5 Fig. 5. Synthesis of different resilience assessment methods

Fig. 6 .

 6 Fig. 6. Partial correlation network of "-ilities" including components for evaluation.

Fig. 9 .

 9 Fig. 9. Resilience Dynamic and "-ilities" mapping


Laurent Navarro

Lara Leclerc

Jérémie Pourchez

Does Acoustic Overlay of Music Improve Aerosol Penetration into Maxillary Sinuses?

Mini Review

Chronic rhinosinusitis (CRS) is a common disorder characterized by mucosal inflammation of the nose and paranasal sinuses.

Recent years have seen numbers of findings and improvements in CRS treatment using nebulization process. Targeting delivery of nebulized antibiotics into the maxillary sinuses, the sites of infection, could improve clinical outcomes in patients with CRS.

Thus, nasal drug delivery by nebulization is widely used in sinus disorders, because of its safety and convenience and due to its advantages as a painless therapy. However, the nebulization conditions to facilitate penetration of aerosols into the sinus cavities are not well established. The practice of aerosol therapy to treat CRS has not been studied thoroughly, despite few works have shown clinical benefit. This paper demonstrates that the music signal superimposed to aerosol provides a considerable innovative solution for the treatment of CRS patients. It encompasses frequency values among which the resonance frequency of the maxillary sinuses of patients regardless the initial sinus anatomy of the patient and the pathology stage and is thus more efficient to deliver the aerosol into the maxillary sinuses.

"Music heals". This adage is generally studied by neuropsychologists and music therapists based on psychological approaches [START_REF] Kemper | Music as therapy[END_REF]. Unfortunately, one knows that it is difficult to prove since it is hardly measurable [START_REF] Evans | The effectiveness of music as an intervention for hospital patients: a systematic review[END_REF]. Moreover, in these studies, music is used traditionally through speakers or headphones as it was designed for. In the meantime, it is well known that music has complex features in terms of signal properties, especially if regarded as a random signal. In short, music belongs to the class of pseudostationarity signals which implies some statistical randomness but also some stationarity. In addition, music has a large frequency spectrum which is mainly linked to the human ear's response of 20Hz to 20kHz. Most of the musical information lies in the 40Hz-16kHz range, and this range depends a lot on the musical style. These characteristics can be exploited when such frequency ranges must be used for medical treatments like nebulization process.

Instead of using ear-fatiguing signals like sinusoidal, or sum of sinusoidal, signals. Then, music can be used for its characteristics as a signal. Patients are more likely to accept the presence and the hearing of a signal if it is music.

Chronic rhinosinusitis (CRS) is a disorder characterized by mucosal inflammation of the nose and paranasal sinuses. This common disease is marked by chronic sinonasal symptoms persisting for greater than 12 weeks that above all diminish patients' quality of life. It is a significant and increasing health problem which results in a large financial burden on society. CRS reportedly affects 5% to 13% of the general population in the United States, Europe and China [START_REF] Agache | Global atlas of allergic rhinitis and chronic rhinosinusitis, 1 st (edn)[END_REF]. Recent years have seen numbers of findings and improvements in CRS treatment using nebulization process [START_REF] Moghadam | Toward smart Nebulization: Engineering acoustic airflow to penetrate maxillary sinuses in chronic rhinosinusitis[END_REF][START_REF] El Merhie | A new strategy to improve drug delivery to the maxillary sinuses: the frequency sweeps acoustic airflow[END_REF]. Targeting delivery of nebulized antibiotics into the maxillary sinuses, the sites of infection, could improve clinical outcomes in patients with CRS. Thus, nasal drug delivery by nebulization is widely used in sinus disorders, because of its safety and convenience and due to its advantages as a painless therapy. Topical delivery of antimicrobial drugs for treatment of CRS also brings intuitive advantages over systemic therapy. It minimizes the risk of systemic side effects, the development of antibiotic resistance in non-targeted areas and allows a high topical drug concentration deposition with a minimal systemic adsorption. The hypothesis to explain this phenomenon was based on the Helmholtz resonator principle. In fact, the sinuses can be seen as cavities opened on a small tube with a relatively constant diameter.

As seductive as it may be, the Helmholtz resonator formula giving the fundamental frequency (Figure 1) is based on few elementary parameters. This simple empirical equation means that in good conditions of sphere volume (i.e. the maxillary sinus cavity in our case), length and diameter of the tube (i.e. the maxillary ostium in our case), one can find a resonance frequency of 100Hz.

However, any geometric variation from this fragile equilibrium can lead to a wide range of different resonance frequencies, which means that using a fixed frequency of 100Hz may be ideal only for very few patients. Looking closely to Figure 1, one can see that the inter-individual anatomical variability existing between patients can lead to large differences in the resulting resonant frequency.

Moreover, even for a same patient with a given geometric features of maxillary sinuses, this resonant frequency can change during the evolution of the CRS. The inflammation and the mucus secretion can decrease the ostium diameter which is more or less obstructed, and the volume of the cavity can also vary due to the more or less fluid-filled sinus (Figure 1). In the past years, strategies have been developed to use varying acoustic frequencies that led to better results concerning penetration of aerosols in the sinuses [START_REF] Moghadam | Toward smart Nebulization: Engineering acoustic airflow to penetrate maxillary sinuses in chronic rhinosinusitis[END_REF][START_REF] El Merhie | A new strategy to improve drug delivery to the maxillary sinuses: the frequency sweeps acoustic airflow[END_REF]. These methods are based on the use of a frequency sweep that allow to reach all possible resonance frequencies within a specific range [START_REF] El Merhie | A new strategy to improve drug delivery to the maxillary sinuses: the frequency sweeps acoustic airflow[END_REF]. To allow for the choice of a wide variety of signals, it has been necessary to develop a specific device consisting of a membrane mounted on a vibrating pot linked to a computer through a power amplifier. This device led us to push the concept of using varying frequencies further while considering the patient's well-being. Considering that music is often associated with certain levels of well-being and enjoying the good properties of such signals, we decided to explore their efficiency for the use in the drug delivery process by nebulization to target the maxillary sinuses (Figure 2). We tested two different musical pieces: "Für Elise" by Beethoven and "Get Lucky" by Daft Punk. The first one is categorized as classical music and is a quite smooth signal with no big amount of low frequencies, but a more complex behavior and few stationarities. The second one can be categorized in popular electronic music and is opposite to the first one with higher level of low frequencies and more stationarity due to the electronic kick beating approximatively two times per second. Using rigorously the same experimental procedure described in [START_REF] El Merhie | A new strategy to improve drug delivery to the maxillary sinuses: the frequency sweeps acoustic airflow[END_REF], the results we achieved exceeded what we expected. The first finding was that Citation: Laurent Navarro, Lara Leclerc, Jérémie Pourchez. Does Acoustic Overlay of Music Improve Aerosol Penetration into Maxillary Sinuses?. On J Otolaryngol & Rhinol. 1(4): 2019. OJOR.MS.ID.000517. musical signals were clearly the best signals for aerosols deposition in sinuses, even at relatively low levels, compared to fixed 100Hz frequency and acoustic sweep frequencies. To do so, we measured in a nasal replica the Sodium Fluoride (NaF) deposition in maxillary sinuses, and we found that music and random noise of frequency range [100-850] were way more efficient to help the aerosol penetrate the sinuses. We measured ten times increase in the deposition for an amplitude of the signal of 80dB.

(Figure 3) Aerosol deposition (using NaF as a chemical tracer) in left maxillary sinus (LMS) for 5 different acoustic configurations: Non-acoustic airflow, Fixed 100Hz sinusoidal acoustic airflow, 100-850 Hz random noise, "Für Elise" and "Get Lucky". Control experiments refers to nebulization of water without NaF chemical tracer. Experimental procedures described in [START_REF] El Merhie | A new strategy to improve drug delivery to the maxillary sinuses: the frequency sweeps acoustic airflow[END_REF].

In the light of results obtained in this study, the music signal superimposed to aerosol provides a considerable innovative solution for the treatment of CRS patients as it encompasses frequency values among which the resonance frequency of the maxillary sinuses of patients regardless the initial sinus anatomy of the patient and the pathology stage. Besides, the music aerosol is also patients-driven to make the aerosol treatment more funny and let them feel more comfortable in order to improve the patient compliance with airborne drug treatment.

  However, the nebulization conditions to facilitate penetration of aerosols into the sinus cavities are not well-established. The practice of aerosol therapy to treat CRS has not been studied thoroughly, despite few works have shown clinical benefit. To enhance the penetration of nebulized particles into badly ventilated areas (i.e. sinuses in healthy subject) or non-ventilated areas (i.e. sinuses in patients with sinus diseases), a pressure gradient generated by an acoustic airflow can be added to a usual nebulizer.The effectiveness of the nebulization process is important because of the huge incidence of CRS, and the cost of the devices used in the process. This implies public authorities' awareness of the problem of efficiency and reimbursement of treatment.Since the 1950s, acoustic airflow superimposed to nebulization process is empirically used as a medical treatment to improve the penetration of aerosols in nasal cavities mainly for the treatment of chronic rhinosinusitis. For long, the principle of sound superimposed to nebulization has been used with more or less success, using a sound which is basically a 100Hz or 50 Hz sinusoidal signal. Historically, this value was found accidentally because of dust found in the sinuses of workers using electrical rotating machines inducing this type of sinusoidal signal. But today, this process is questioned by numerous studies and experiments.

Figure 1 :

 1 Figure 1: Helmholtz Resonator Formula Where V is the Sound Speed in Air, And A, L and V Respectively the Section and the Length of the Tube, and the Volume of the Cavity.

Figure 2 :

 2 Figure 2: Principle of Music Aerosols. The Musical Signal Is Superimposed to The Aerosol to Improve the Penetration in the Maxillary Sinuses.

Figure 3 :

 3 Figure 3: Aerosol Deposition (Using Naf As A Chemical Tracer) in Left Maxillary Sinus (LMS).

Acknowledgement

None.

Conflict of Interest

No conflict of interest.


E Krichen

A Rapaport

E Le Floc'h

E Fouilland
email: eric.fouilland@cnrs.fr

Demonstration of facilitation between microalgae to face ammonia toxicity

Positive interactions such as facilitation play an important role during the biological colonization and species succession in harsh or changing environments. However, the direct evidence of such ecological interaction in microbial communities remains rare. Using common freshwater microalgae isolated from a High Rate Algal Pond (HRAP) treating wastewaters, we investigated with both experimental and modelling approaches the direct facilitation between two algal strains during the colonization phase. Our results demonstrate that the first colonization by microalgae under a severe chemical condition arose from the rapid growth of pioneer species such as Chlorella sorokiniana, which facilitated the subsequent colonization of low growth specialists such as Scenedesmus pectinatus. The pioneer species rapidly depleted the total available ammonia nitrogen favouring the specialist species initially inhibited by free ammonia toxicity. This latter species ultimately dominated the algal community in accordance with the competitive exclusion under low nutrient conditions. We show that microbial successions are not only regulated by climatic conditions but also by interactions between species based on the ability to indirectly modify their growth conditions. Furthermore, the theoretical study of algal resilience and succession times as proxies of the facilitation efficiency showed that control of algal production processes might be possible by modifying the initial populations' densities.

Introduction

One of the major challenges in microbial ecology is to understand the dynamics of communities of interacting species. Understanding the biological interactions and the time scales over which they occur is necessary to interpret the results of the directional succession process of communities' development in the natural environment and in artificial ecosystems. In aquatic systems, microalgae are present in natural waters such as oceans, lakes, rivers, and ponds and play a prominent role in the marine and fresh-water ecosystems where they drive major ecosystem processes. Strong similarities exist between marine and freshwater phytoplankton ecology [START_REF] Kilham | Comparative ecology of marine and freshwater phytoplankton1[END_REF] when they face similar change in growth conditions leading to temporal species succession. Abiotic forcing and biotic interactions can both result in successional trends in phytoplankton. The scientific discussion around the phytoplankton growth periodicity and succession has been dominated by the role of the environmental drivers including global climatic change (e.g. light, temperature, wind) [START_REF] Levasseur | Hierarchical control of phytoplankton succession by physical factors[END_REF][START_REF] Barbiero | The effects of disturbance events on phytoplankton community structure in a small temperate reservoir[END_REF][START_REF] Grover | Seasonal dynamics of phytoplankton in two warm temperate reservoirs: association of taxonomic composition with temperature[END_REF][START_REF] Lewandowska | Climate change and the spring bloom: a mesocosm study on the influence of light and temperature on phytoplankton and mesozooplankton[END_REF][START_REF] Deng | Effects of nutrients, temperature and their interactions on spring phytoplankton community succession in Lake Taihu, China[END_REF] , local hydrological variations [START_REF] Gaedeke | The influence of the frequency of periodic disturbances on the maintenance of phytoplankton diversity[END_REF][START_REF] Nõges | Water level as the mediator between climate change and phytoplankton composition in a large shallow temperate lake[END_REF] biological disturbances such as species invasion [START_REF] Robinson | Does Invasion Sequence Affect Community Structure?[END_REF] , and chemical effects such as toxic pollutants, nutrient enrichment, or change in 7, 10, 11, 6, 12 . On the other hand, the conditions governing phytoplankton growth over the seasonal change in plankton communities have mostly been discussed in the context of algae-grazer interactions (e.g. Porter, 1977) [START_REF] Porter | The Plant-Animal Interface in Freshwater Ecosystems: Microscopic grazers feed differentially on planktonic algae and can influence their community structure and succession in ways that are analogous to the effects of herbivores on terrestrial plant communities[END_REF] or exploitative competition (e.g. Tilman, 1982) [START_REF] Tilman | Resource Competition and Community Structure[END_REF] . However, few studies have discussed the role of positive interactions (i.e. facilitation), which is the main driving biotic mechanism in plant community succession, particularly under harsh environmental conditions [START_REF] Stachowicz | Facilitation, and the Structure of Ecological Communities Positive interactions play a critical, but underappreciated, role in ecological communities by reducing physical or biotic stresses in existing habitats and by creating new habitats on which many species depend[END_REF] . The ability to colonize a specific habitat usually explains the dominance and succession of some species under the change in nutrient and/or mixing conditions (see [START_REF] Margalef | Life-forms of phytoplankton as survival alternatives in an unstable environment[END_REF][START_REF] Smayda | Phytoplankton species succession[END_REF][START_REF] Litchman | The role of functional traits and trade-offs in structuring phytoplankton communities: scaling from cellular to ecosystem level[END_REF] ). In marine ecosystems, small-cell diatoms usually grow rapidly in a first stage after a strong nutrient enrichment because of their higher growth rates and are then followed by larger-cell diatoms and dinoflagellates, which are more likely to occur when nutrients are depleted [START_REF] Margalef | Life-forms of phytoplankton as survival alternatives in an unstable environment[END_REF][START_REF] Smayda | Phytoplankton species succession[END_REF] . The seasonal patterns of succession in freshwater ecosystems might be explained by the first occurrence of invasive small-sized stress-tolerant competitor species followed by disturbance-tolerance ruderal species [START_REF] Anneville | Temporal mapping of phytoplankton assemblages in Lake Geneva: Annual and interannual changes in their patterns of succession[END_REF] .

Because phytoplankton can substantially change its physical and chemical conditions of growth (e.g. by decreasing transparency, increasing , or depleting key nutrients), we suggest that this phytoplankton-driven environmental modification can provoke shifts in assemblages of species, thus leading to successions. Hence, we suppose that under highly polluted conditions, similar to strongly anthropized ecosystems, an assemblage of typical pioneer species will first develop because of their potential for rapid dispersal and growth. Species showing the fastest growth rates and the strongest stress tolerance to harsh environments will be able to grow under such conditions, making the ecosystem more favourable for species that are more competitive in stable growth condition through ecological facilitation. Previous results from a study investigating the biological succession within HRAPs used for wastewater treatment showed a rapid and initial growth of Chlorella sp. followed by a low-growth of species Scenedesmus sp. [START_REF] Galès | Importance of ecological interactions during wastewater treatment using High Rate Algal Ponds under different temperate climates[END_REF] . Similar successions have been observed in other studies using HRAPs as well [START_REF] Canovas | Seasonal development of phytoplankton and zooplankton in a high-rate algal pond[END_REF][START_REF] Cho | Microalgal diversity fosters stable biomass productivity in open ponds treating wastewater[END_REF] . The successional trends of typical microalgal species growing in HRAPs have generally been interpreted as responses to predation and/or seasonal factors [START_REF] Schlüter | Impact of rotifer grazing on population dynamics of green microalgae in high-rate ponds[END_REF][START_REF] Canovas | Seasonal development of phytoplankton and zooplankton in a high-rate algal pond[END_REF] . We hypothesized that during the colonization phase of HRAPs supplemented with wastewaters, Chlorella is able to modify its habitat and facilitate growth conditions for Scenedesmus by reducing the nutrient stress modulated by free ammonia toxicity [START_REF] Abeliovich | Toxicity of ammonia to algae in sewage oxidation ponds[END_REF] . Therefore, we suggest that microbial successions might not be regulated by climatic conditions only, but also through positive interactions between species facing external chemical stress. We conducted a set of laboratory experiments using the species Chlorella sorokiniana and Scenedesmus pectinatus, isolated from the HRAP [START_REF] Galès | Importance of ecological interactions during wastewater treatment using High Rate Algal Ponds under different temperate climates[END_REF] , to determine the inhibiting factor among ammonium ion, , and free ammonia and to determine their respective effects on the growth rates of each species. Then we used a modelling approach to test the magnitude of facilitation/competition on the two microalgae and, further, to explain the observed patterns in HRAPs continuously supplemented with wastewaters. Finally, we studied the resilience and succession times providing informative proxies on the efficiency of the ecological facilitation and the successional trends depending on the initial populations' densities. Our conclusions supported the theoretical considerations of ecological facilitation between one tolerant and one sensitive organism to a gradient of resource toxicity/bioavailability.

Results and Discussion

Three series of experiments denoted , , and were performed i) to isolate the inhibitory effects of possible external factors such as high nitrogen concentrations or and ii) to demonstrate a facilitation interaction between two species. We then show how to exploit the data using a mathematical modelling approach, providing new insights on the facilitation phenomenon.

No direct toxic effect of high ammonium and on microalgae growth rates. Chemical factors such as Total Ammonia Nitrogen (

) and can affect the rate and efficiency of photosynthesis of microalgae [START_REF] Goldman | The effect of pH in intensive microalgal cultures. I. Biomass regulation[END_REF][START_REF] Källqvist | Assessment of ammonia toxicity in tests with the microalga, Nephroselmis pyriformis, Chlorophyta[END_REF][START_REF] Wang | Ammonium Nitrogen Tolerant Chlorella Strain Screening and Its Damaging Effects on Photosynthesis[END_REF] . Negative effects of (referring to nitrogen in two distinct forms: ammonium ion and free ammonia ) on algal growth and physiology might occur and vary significantly within classes of microalgae and within species (see [START_REF] Collos | Acclimation and toxicity of high ammonium concentrations to unicellular algae[END_REF] ). The photosynthesis of different species of marine diatoms was severely inhibited at concentrations in the range of 0.5 to 11 29, 30 . At low values (<8), toxicity is likely associated with , while at alkaline values (>8), cell growth inhibition is rather due to . During the first set of experiments , the potential toxicity of high ammonium ion was investigated for the two isolated algal species when values were adjusted to 7.5 at 25°C. Hence, under such conditions, we ensure that 98% of (ranging from 10 to 110 ) was present as form. Under this range of concentrations, no significant difference in the growth rates of Scenedesmus pectinatus or Chlorella sorokiniana was measured (p>0.05, ANOVA from ANOCOVA test results; see Figure 1a). Therefore, the form at such concentrations, typically found in wastewaters, did not affect the growth rates of both microalgae. Similarly, it was reported that species such as Chlorella are very tolerant to high concentrations (max. 140 and 250 stated respectively in Collos and Harrison (2014) [START_REF] Collos | Acclimation and toxicity of high ammonium concentrations to unicellular algae[END_REF] and Tam and Wong (1996) [START_REF] Tam | Effect of ammonia concentrations on growth of Chlorella vulgaris and nitrogen removal from media[END_REF] ). However, Przytocka-Jusiak et al. (1977) [START_REF] Przytocka-Jusiak | Properties of Chlorella vulgaris strain adapted to high concentration of ammonium nitrogen[END_REF] reported that cell division of was inhibited at greater concentrations (> 300 , although such concentrations did not cause any visible lethal effect. The studies performed on Scenedesmus accuminatus showed that cell growth was inhibited only when concentrations were higher than 200

33

. Interestingly, it has been previously reported that algal photosynthesis of was inhibited at above 28 if the culture exceeded 8.0 [START_REF] Goldman | The effect of pH in intensive microalgal cultures. I. Biomass regulation[END_REF] . Because can vary during algal growth in ecosystems due to the rapid and large consumption of microalgae, this might directly or indirectly affect algal growth rates. The optimal of many freshwater algae is about 8 [START_REF] Kong | Culture of microalgae Chlamydomonas reinhardtii in wastewater for biomass feedstock production[END_REF] . The growth of many algal species is inhibited in waters at greater than 8 (reduction of productivity of Chaetoceros sp. and Chlorella sp. by 22% when was raised from 8 to 9), while other species can grow well above 8 (e.g. Amphora sp. and Ankistrodesmus sp. at 9 and 10, respectively) [START_REF] Weissman | Photobioreactor design: mixing, carbon utilization, and oxygen accumulation[END_REF] . High conditions limit the availability of while dominates, and then algae cannot efficiently accumulate carbon and require a high supply of carbonates for maintaining photosynthetic activity [START_REF] Moroney | Effect of carbonic anhydrase inhibitors on inorganic carbon accumulation by Chlamydomonas reinhardtii[END_REF] or reducing the affinity to free 37, 38 . During the second set of experiments , the direct effect of was tested using values ranging from 6 to 9 on algal growth under low initial concentration of about 1 . As shown in Figure 1b, the growth rates measured for both species, S. pectinatus and C. sorokiniana, were not significantly different for all the tested conditions (p>0.05, ANOVA from ANOCOVA test results). Then, similar to high values of , the results did not support the hypothesis of a negative effect of high values on microalgae growth rates. Thus, we assume that our results are consistent with the early study of Azov and Goldman (1982) [START_REF] Azov | Free ammonia inhibition of algal photosynthesis in intensive cultures[END_REF] suggesting that did not play a role in the magnitude of inhibition but in the degree of dissociation of nontoxic ammonium to toxic free ammonia . In other words, the dissociation of as a function of is the main determinant of how much is available to inhibit photosynthesis. Hence, assuming that concentrations in and were likely too low to exhibit algal growth inhibition, the effect of free ammonia at higher concentrations was then tested on both species.

Evidence of species-dependent ammonia effect.

is considered the 's most toxic form for aquatic organisms [START_REF] Haywood | Ammonia toxicity in teleost fishes: a review[END_REF] . The third set of experiments was then performed on our algal isolates from the HRAP to test algal growth under concentrations ranging from 0.56 to 29.42 . The results for the growth rates of both isolates are represented in Figure 1c and showed that the growth rates of C. sorokiniana measured under the different unionized ammonia concentrations were similar (p>0.05, ANOVA from ANOCOVA test results). However, the growth rates of S. pectinatus were significantly different (p<0.05, ANOVA from ANOCOVA test results) with an important reduction in growth rates when exceeded 8.7 Similarly, early works reported that free ammonia at concentrations greater than 15 and at values over 8 inhibited the photosynthesis and growth of Scenedesmus obliquus [START_REF] Abeliovich | Toxicity of ammonia to algae in sewage oxidation ponds[END_REF][START_REF] Azov | Free ammonia inhibition of algal photosynthesis in intensive cultures[END_REF] . A strong inhibition of Chlorella sorokiniana was previously observed at about 77 of free ammonia [START_REF] Muñoz | Photosynthetically oxygenated acetonitrile biodegradation by an algal-bacterial microcosm: a pilot-scale study[END_REF] , although the resistance of Chlorella sorokiniana to high concentrations (326 ) was also previously reported [START_REF] Ogbonna | Treatment of high strength organic wastewater by a mixed culture of photosynthetic microorganisms[END_REF] , suggesting that species can also adapt their metabolism and becoming more tolerant to high environments over time. In HRAPs initially supplemented with high concentrations, toxicity is therefore expected to be associated with elevated due to intense photosynthetic activity and could cause the depletion of microalgae culture or promote replacement with other tolerant species to face the prevailing stress. This feature should be magnified considerably during the summer as the conversion between and is also temperature dependent. Evidence of facilitation interactions through a modelling approach. A modelling approach was used to identify the growth characteristics for each species in order to predict their dynamics when they are growing together. We assumed that was the sole limiting substrate driving the algal growth and would have a direct inhibitory effect on cell growth as a function of , , and temperature ( -) [START_REF] Emerson | Aqueous ammonia equilibrium calculations: effect of pH and temperature[END_REF] . Thus, as a first step, species growth rates were related to external concentrations to calibrate one kinetic model, which could represent satisfactorily most of the data points of the previous test experiments obtained in and . The proposed model was inspired from Aiba-Edward's model [START_REF] Edwards | The influence of high substrate concentrations on microbial kinetics[END_REF] describing the substrate inhibition at high concentrations and consisting of a modified version of the Monod equation, but here it has a slightly different mathematical expression as explained below. While Monod kinetics assumed that only one nutrient limits the growth of cells, the model we propose here includes that a by-product of this limiting nutrient (free ammonia -) negatively affects cells growth as given by the following expression:

(*)

where is the maximum growth rate ( ), is the affinity to substrate ( ), and is the inhibition constant of free ammonia nitrogen (

). This growth function provided a good fit to experimental data describing the growth kinetics of the two species (see Figure 2). The identified kinetic parameters are given in Our results are in accordance with older chemostat experiments comparing Scenedesmus acutus and Chlorella minutissima under P-limited growth [START_REF] Sommer | Comparison between steady state and non-steady state competition: Experiments with natural phytoplankton: Phytoplankton competition[END_REF] . The ecological succession of species presenting Monod-and Haldane-kind growth functions have already been shown theoretically [START_REF] Harmand | Biological control of the chemostat with nonmonotonic response and different removal rates[END_REF] but not yet experimentally. The Monod and Haldane kinetics were fitted to our data (results not shown). Their graphs closely resemble those given by (*), but with a higher criterion J.

Knowing the growth performances of each species in the laboratory (Figure 3a), we proposed a predictive model to explore how the assemblage of the two species might react under a fixed (8.6) and temperature (25°C) in continuous culture to check if the hypothesis of ecological facilitation is verified. We used the initial conditions of substrate and biomass and the operational conditions (dilution rate and input substrate concentration) encountered in the previous HRAP study [START_REF] Galès | Importance of ecological interactions during wastewater treatment using High Rate Algal Ponds under different temperate climates[END_REF] . Our results demonstrated that S. pectinatus could not be maintained and is washed out because of the toxicity when cultivated alone (Figure 3b). The mathematical simulations predicted that when both microalgae are introduced together, C. sorokiniana grows rapidly first while the growth of S. pectinatus is inhibited because of high 3c).

Validation of facilitation interactions in HRAP.

The dynamics of the biomass of Chlorella sp. and Scenedesmus sp. and the concentrations measured in HRAP operating from 28 April 2015 to 8 September 2015 in Northern France [START_REF] Galès | Importance of ecological interactions during wastewater treatment using High Rate Algal Ponds under different temperate climates[END_REF] were compared to model simulations (see Figure 4) using the growth functions represented in Figure 2 and Table 1. Some few changes to the previously simulated model were done to take into account the complexity of the biological processes due to the presence of other consumers (e.g. heterotrophic bacteria taking up nitrogen resource) and predators (reducing algal biomass). Indeed, we have added mortality terms to account for the grazing effect on each algal species in an indirect way, keeping the model as simple as possible. Knowing that bacteria were also growing in the pond and consuming nitrogen [START_REF] Galès | Importance of ecological interactions during wastewater treatment using High Rate Algal Ponds under different temperate climates[END_REF] , we supposed that yield coefficients ranged between i) minimal values theoretically calculated during the period of type peak of biomass reached by each species in the HRAP (i.e. 1.3±0.1 gC/gN and 0.5±0.2 gC/gN for Chlorella sp. and Scenedesmus sp., respectively) and ii) maximal values identified in our laboratory chemostat experiments at 3 days steady state (i.e. 5.93±0.66 gC/gN and 4.98±0.58 gC/gN for C. sorokiniana and S. pectinatus, respectively). The estimated parameters of yield and mortality coefficients obtained from the comparison of the model dynamics with data from HRAP are represented in Table 2. The identification results appear to be realistic. Assuming that higher predation pressure corresponds to a higher mortality coefficient, our results suggest that Chlorella was likely more sensitive to grazing than Scenedesmus known to produce grazer-morphological defense [START_REF] Mayeli | The efficacy of Scenedesmus morphology as a defense mechanism against grazing by selected species of rotifers and cladocerans[END_REF] . However, the washout of Chlorella at the system steady state is not due to high pressure by a high mortality coefficient but rather to competition with Scenedesmus when the environment is depleted of nitrogen resources, as demonstrated through the previous simulation results (see Figure 3c). We noted that the estimated yields coefficients in chemostat experiments were higher than the identified ones in the HRAP which may be explained by the presence of denitrifying bacteria in the HRAP producing N 2 subsequently lost through degassings [START_REF] Galès | Importance of ecological interactions during wastewater treatment using High Rate Algal Ponds under different temperate climates[END_REF] . The present results confirmed the initial hypothesis that the colonization of hypertrophic ecosystems by pioneer species such as Chlorella is a prerequisite for the development of other organisms. Chlorella species are usually considered as an invasive phytoplankton or pioneer species because they maintain fast growth rates and assimilate resources with short generation times, and they are able to dominate over slower-growing species [START_REF] Elliott | An investigation of dominance in phytoplankton using the PROTECH model[END_REF][START_REF] Reynolds | Environmental requirements and habitat preferences of phytoplankton: chance and certainty in species selection[END_REF] . We show here that such pioneer organisms can modify their chemical environment by reducing ammonia toxicity, and then the growth of the sensitive microalgae Scenedesmus sp. becomes more efficient than expected in monoculture. At low and nontoxic nutrient levels, Scenedesmus is considered an affinity specialist [START_REF] Sommer | Comparison between steady state and non-steady state competition: Experiments with natural phytoplankton: Phytoplankton competition[END_REF] , and it is able to dominate in HRAP over Chlorella and colonize the HRAP.

There are different advantages to having a Scenedesmus dominance in an HRAP supplemented with wastewaters, as this species possesses a high affinity to nitrogen, is strongly resilient to predators, and is readily settleable when the harvested biomass is used for different purposes (e.g. lipid production [START_REF] Wong | Scenedesmus quadricauda for Nutrient Removal and Lipid Production in Wastewater[END_REF] ). Using the mathematical approach, we investigated the influence of the initial density of both species on the time requested for rapid development of Scenedesmus in HRAP that might be useful to further explore the optimization strategies under external stress.

Table 2. Calibration results on HRAP data (continuous cultures).

Influence of initial biomass values on resilience and succession time.

We defined the resilience time as the duration for Scenedesmus to reach its initial biomass value under the presence of the toxic concentrations. Because the succession of the two microalgae is required for maintaining Scenedesmus, we also defined the succession time as the duration for which the species have the same density level for the second time owing to the predominance of Scenedesmus. The iso-values diagrams of the resilience time and the succession time are presented in Figure 5 and are obtained for different initial microalgae biomass conditions. The resilience time is more affected by the initial concentrations of Chlorella than by the initial biomass concentrations of Scenedesmus Figure 5a. This contrasts with the succession time that is more sensitive to initial Scenedesmus biomass, especially when the Chlorella biomass is initiated at values ≥1 mgC.L -1 . Such simulation would be of interest in further control of the diversity within a HRAP supplemented with wastewaters, especially for managing the periods of dysfunction (e.g. sudden algal crash, variations in wastewaters inflow could be suggested to increase the initial concentration of Chlorella (at a concentration higher than 5 mg L -1 ) through bioaugmentation to ensure a rapid reduction of NH 3 toxicity and rapid development of Scenedesmus in a minimum of 16 days. On the other hand, the time needed for Scenedesmus predominance over Chlorella will depend on the initial concentration of Scenedesmus and the higher the Scenedesmus initial concentration would be (>12 mg L -1 ) the faster the succession would occur (minimum of 60 days). Consequently, we evidence that the algal resilience and succession times within an intensive algal ecosystem are strongly depending on the initial populations' densities that may be used to control algal production processes.

Materials and Methods

HRAP experiment. The pre-existing data used in this study were obtained in HRAP of 1.9 m 3 working volume, continuously fed by pre-treated wastewaters (after screening and removing grit, sand, and grease) with a constant retention time of 6 days (see [START_REF] Galès | Importance of ecological interactions during wastewater treatment using High Rate Algal Ponds under different temperate climates[END_REF] ). Algal blooms occurred naturally in the open pond without any algal inoculation. The period covered by this study was from 28 April 2015 to 8 September 2015. For the present study, we used the data obtained through analytical monitoring that was performed on the influent wastewater and on samples taken from the HRAP. They included water temperature, chemical analyses ( and ), and the algal biomass of the two dominant algal species (Chlorella sp and Scenedesmus sp) estimated using cell count from flow cytometry and converted into carbon units.

Microalgae strains, cultivation conditions, and laboratory experiments. Strains of freshwater microalgae Chlorella sp. and Scenedesmus sp. were isolated from the HRAP samples taken in October 2015. Individual strains were isolated in Z8 media [START_REF] Kotai | Instructions for preparation of modified nutrient solution Z8 for algae[END_REF] . The Z8 media was modified replacing all nitrogen forms with ammonium salt (NH 4 Cl) as the sole source of nitrogen in the growth medium and by adding the HEPES buffer at 20 mM. The two species were maintained and cultivated under continuous light (100 μE m -2 s -1 ) and temperature (20°C). We performed three series of experiments ( , and ) in batch reactors with a working volume of 40 mL. Each series were preceded by a pre-incubation phase in which the two species are preadapted to the fixed cultivation conditions in each set of experiments and providing sufficient fresh volumes for inoculations. The pre-incubations were performed either in continuous mode (in 2L photobioreactors stirred at 300rpm, one-sided illumined at 130 μmolm -2 s -1 , before

) or in batch mode (in a shaken flask at 150 rpm of 200 mL, before and ). All batch experiments (in preincubation or in the three-test series) were performed in laboratory incubators under a temperature set at 25°C ± 2°C, an orbital agitation at 150 rpm speed and the incident light intensity at 50 μmolm -2 s -1 in and . The first pre-incubation in continuous photobioreactors were performed to determine the yield constants and provide sufficient fresh volumes for later inoculation in batch culture. Thus, each strain was growing for about 15 days until the biomass stabilization, under a constant temperature of 25°C and a continuous supply of sterilized medium (C:N substrate ratio at about 1:1 and N:P substrate ratio at about 34:1) at a fixed value of 7.5 and a fixed dilution rate (0.25 d -1 ). After that, the growth of the two species was assessed in batch cultures (as described above) under an initial concentration ranging from 10 to 110 mg.L -1 keeping constant the concentrations of the other medium components. The value was maintained at 7.5 in all batch reactors of . In the second series of experiments , prior to the experiment, the two species were pre-incubated in batch cultures for about 6 days in a sterilized medium of modified Z8-NH4 with a C:N substrate ratio at about 88:1 and N:P substrate ratio at about 2:1 and were set at 7.5. Then, SE2 experiments were performed (as described above) under different conditions initially adjusted to 6.0, 6.5, 7.0, 7.5, 8.0, 8.4, 8.7, and 9.0 with NaOH or HCl while using a similar initial concentration of NH 4 Cl of 2 mg.L -1 that was assumed to be nontoxic for both microalgae strains. Prior , the 6-days pre-incubation of two species was performed in a sterilized medium of modified Z8-NH 4 with C:N ratio substrate at about 88:1 and N:P substrate ratio at about 8:1 at a fixed value initially set at 8.6 (corresponding to the average measured in HRAP). Finally, in , the growth of the two species was assessed in batch cultures under a large range of initial NH 4 Cl from 1.2 to 187.7 mg.L -1 .

DNA isolation, PCR, and sequencing. Genomic DNA was extracted from a 10-mL sample filtered onto a 0.2 μm membrane (PALL Supor® 200 PES), using the phenol/chloroform method. The 18S and ITS rDNA were amplified in PCR reactions using the Pfu polymerase (Promega) with the primers EAF3 and ITS055R [START_REF] Pröschold | Molecular phylogeny and taxonomic revision of Chlamydomonas (Chlorophyta). I. Emendation of Chlamydomonas Ehrenberg and Chloromonas Gobi, and description of Oogamochlamys gen. nov. and Lobochlamys gen[END_REF] . The PCR products were purified and sequenced using specific primers to target the variable V4 region of the 18S rDNA as well as the ITS region. Sanger sequencing was performed at Eurofins Genomics (GATC services).

Sample analyses.

The in each culture solution was determined daily ( meter Symphony® SP70P, VWR). For algal biomass estimation, samples were shaken to bring all the cells into suspension and subsamples were daily taken to measure absorbance. In , the growth of algae was measured using optical density (OD) of the culture with a microplate reader (FLUOSTAR®, BMG Labtech) at 650 nm. In SE2 and SE3, cell mass was measured by fluorescence (EX 450 nm, EM 680 nm) and optical density (OD) at 650nm, 730 nm, and 680 nm using a microplate reader (CHAMELEON®, Hidex).

In and , subsamples were collected at the beginning and at the end of each experiment, for nutrient and biomass analysis. Samples were then filtered using i) 0.2µm Sartorius filters for measuring nutrients in filtrates and ii) pre-combusted AE filters for measuring carbon biomass onto filters. Ammonia nitrogen was measured with a spectrophotometric test kit (SpectroQuant®, Merck Millipore) and orthophosphate phosphorus according to an optimized molybdenum blue method [START_REF] Aminot | Hydrologie des écosystèmes marins: paramètres et analyses[END_REF] . After drying the filters (24h, 60°C), the particulate organic carbon representing mainly algal carbon biomass was analysed using an ANCA mass spectrometer (Europa Scientific). Data Analysis. We performed the covariance analysis using the "aoctool" function of Matlab to compare significant differences in growth rates µ of algae after 48h exposure at each tested condition. The technique required the grouped data of logarithm of the biomass ln(x) measured at time t (during the time period 0 to 48h) for all tested condition. We modelled ln(x) as a linear function of time t to determine whether the slope of the line, which represents an estimate of µ, varies among groups. Based on the model fit of the separate-lines model, the stats output structure from "aoctool" served as input to the multi-compare test "multiconpare" function of Matlab, which allows for testing either slopes or intercepts.

Model description and calibration procedures.

The first identifications of the growth function parameters for the two species were performed by fitting the kinetic model (*) to the assessed values of specific growth rate data obtained in and for which cultivation conditions are either identical or different but would not be disruptive of the growth rates except for the initial concentration. The optimal growth parameters were calibrated by the "fmincon" function of Matlab optimization toolbox used in minimizing a mean square criterion , where and are the normalized experimentally estimated and model generated values of growth rates at the i th experimental condition, and n is the total number of estimated growth rates corresponding to the total number of tested conditions concentrations in and . Secondly, we used the identified growth parameters and the conversion constants , theoretically calculated at the steady state of the continuous photobioreactors (performed at preincubation for ) (by where and are the algal biomass concentration (mgC.L -1 ) and the concentration (mgN.L -1 ) at steady state and is the inlet concentration) to simulate the following model in order to explore the species dynamics under a fixed (8.6) and temperature (25 °C) in a homogeneous continuous reactor. This set of equations gives the variations over the time of both algal biomass of C. sorokiniana and S. pectinatus (in mgC.L -1 ) and substrate concentrations ( = + ) (in mgN.L -1 ), denoted and , respectively. Growth kinetics and of the two species depend on , which is the sole source of nitrogen and supplied continuously at fixed dilution rate =0.16 d -1 and a mean concentration value of = 62.54 mgN.L -1 encountered in the studied HRAP. The model

Figure 1 .

 1 Figure 1. Growth rates from multiple comparisons Matlab tests on growth rate values estimated based on ANCOVA analyses for (in red) and (in blue) at different initial conditions of concentrations (a), (b), and concentrations (c).

Figure 2 .

 2 Figure 2. and data sets (full points) compared to the Kinetic model for C. sorokiniana (continuous red line) and for S. pectinatus (continuous blue line). Data points are the mean of 3 duplicate measurements of growth rate µ.

Figure 3 .

 3 Figure 3. Simulation results obtained under a continuous supply with a high nitrogen concentration (dotted line in (b) & (c)) at a fixed dilution rate (dotted line in (a)). The biomass dynamics of C. sorokiniana and S. pectinatus are represented in solid red lines and solid blue lines, respectively. The substrate dynamics of is represented with a solid black line while the toxic form ( ) is represented with black dashed lines. (a) growth functions identified in Figure 2, (b) S. pectinatus cultivated alone, (c) S. pectinatus growing with C. Sorokiniana.

Figure 4 .

 4 Figure 4. HRAP data points compared to the model prediction (continuous lines). Algal biomasses of Chlorella sp. (in red) and Scenedesmus sp. (in blue) are grown under a fluctuating continuous supply of nitrogen (dotted black line). The growth of the two microalgae is limited by nitrogen concentration in the pond (in black) and sensitive to free ammonia (in magenta).

Figure 5 .

 5 Figure 5. Isovalue diagrams of the times of resilience (a) and succession (b) (in days) depending on the initial biomass densities of Chlorella (CHL) and Scenedesmus (SCE) (in mgCL -1 ) under a continuous supply of high nitrogen concentration.

Table 1 .

 1 The species S. pectinatus showed a strong affinity for nitrogen would grow well at high nitrogen concentrations and would also tolerate high concentrations as reported by its highest inhibition constant ( 130.25 -), while S. pectinatus would grow best at low nitrogen concentrations but would show a much faster decline in growth because of its high sensitivity to ammonia toxicity represented by a low(2.31

	-	).

with a greater ratio than that obtained for C. sorokiniana. In contrast, this latter species has a maximum growth rate (1.04 ) much higher than S. pectinatus (0.58 ). Consequently, C. sorokiniana

Table 1 :

 1 Calibration results on and growth data obtained in batch cultures.

  ). For example, it

	Parameters	C. sorokiniana ( )	S. pectinatus ( )
	(	)	3.91	0.32
	(	)	0.504	0.004
	(least squares criterion)	102.38

Acknowledgments

We thank Elodie Lanouguère for microalgae isolation and cultivation, Ariane Atteia for identifying the microalgal strains, Martine Fortune for ammonia analyses, Patrick Raimbault for carbon content analyses, and Christine Felix for giving helping hand to experiments monitoring. We would also like to thank Bénédicte Fontez for assistance with statistical analyses, and Jérôme Harmand for fruitful comments and discussions during the Seminar on resource-consumer models (21-25 September 2015). This work was supported by the ADEME French Agency and the LabEx NUMEV incorporated into the I-Site MUSE funded by the French Research Agency (ANR) that have both funded the PhD grant of the first author. This study was also supported by the PHYCOVER project, which was funded by the French National Agency for Research (ANR-14-CE04-0011).

was solved using ode23t differential equation solver using the following initial conditions of substrate and biomass: N 0 = 104.50 mgN.L -1 , A 10 =0.0123 mgC.L -1 , A 20 =0.2698 mgC.L -1 .

Third, we validated the hypothesis of ecological facilitation on real dynamics in HRAP. We used the whole dynamics simulated over the time from the given initial condition until the system was about to reach a steady-state and we compared data to the following model equations including terms of mortality and on and

We considered the variations over the time of , and implemented into the model with interpolations performed between the real data points measured over time. We identified the unknown parameters ( , , and ) of the dynamic model using "fmincon" function of Matlab optimization toolbox. Optimal parameters assuring the best fit to data were defined in predefined intervals of boundary values after 100 consecutive estimations. The mean squared error was used as the criterion function for the model parameters estimation and was calculated as the square root of the variance of the observations (of , and ) and divided by the number of measurements.

Author Contributions

A. R, E. L. F, and E. F participated actively in conceiving the experiments, coordinated the research work, and critically revised the manuscript. E. K designed and conducted laboratory experiments, analyzed data and performed mathematical simulations, and wrote the manuscript.