Dominique Pontier
email: dpontier@biomserv.univ-lyon1.fr

David Fouchet
email: fouchet@biomserv.univ-lyon1.fr

Joël Bried
email: joelbried@yahoo.com

Can cat predation help competitors coexist in seabird communities?

Keywords: oceanic islands, seabirds, feral cats, nest site availability, date of arrival, community structure, predator-prey relationships, model

On oceanic islands, nest site availability can be an important factor regulating seabird population dynamics. The potential for birds to secure a nest to reproduce can be an important component of their life histories. The dates at which different seabird species arrive at colonies to breed will have important consequences for their relative chances of success.

Early arrival on the island allows birds to obtain nests more easily and have higher reproductive success. However, the presence of an introduced predator may reverse this situation. For instance, in the sub-Antarctic Kerguelen archipelago, early-arriving birds suffer heavy predation from introduced cats. Cats progressively switch from seabirds to rabbits, since the local rabbit population starts to peak after early-arriving seabird species have already returned to the colony. When late-arriving birds arrive, cat predation pressure on seabirds is thus weaker. In this paper, we investigate the assumption that the advantage of early nest monopolization conferred to early-arriving birds may be counterbalanced by the cost resulting from predation. We develop a mathematical model representing a simplified situation in which two insular seabird species differ only in their arrival date at the colony site and compete for nesting sites. We conclude that predation may ensure the coexistence of the two bird species or favor the late-arriving species, but only when seasonal variations in predation pressure are large. Interestingly, we conclude that arriving early is only favorable until a given level where high reproductive success no longer compensates for the long exposure to strong predation pressure. Our work suggests that predation can help maintain the balance between species of different phenologies.

A c c e p t e d m a n u s c r i p t 1. Introduction

Nests are fundamental resources for many species. In seasonally breeding species, competition for nesting sites may depend on the date at which individuals arrive at the site, with early-arriving individuals theoretically able to secure higher quality territories than laterarriving ones [START_REF] Pulliam | Sources, sinks and habitat selection: a landscape perspective on population dynamics[END_REF][START_REF] Kokko | Competition for early arrival in migratory birds[END_REF]. Several studies on different taxa that face strong competition for breeding territories -including insects (e.g., [START_REF] Wang | Inter-male competition for high-quality host-plants: The evolution of protandry in a territorial grasshopper[END_REF], birds (e.g., [START_REF] Rowan | Regulation of sea-bird numbers[END_REF][START_REF] Greenwood | The natal and breeding dispersal of birds[END_REF] and mammals [START_REF] Bried | Seabird habitat restoration on Praia Islet, Azores archipelago[END_REF] -have supported this hypothesis. Such competition can be inter-species (e.g., [START_REF] Quintana | Competition for nest sites between kelp gulls (Larus dominicanus) and terns (Sterna maxima and S. eurygnatha) in Patagonia[END_REF], intra-species (e.g., [START_REF] Rowan | Regulation of sea-bird numbers[END_REF][START_REF] Candolin | Correlation between male size and territory quality: consequence of male competition or predation susceptibility?[END_REF], or both intraand inter-species (e.g., [START_REF] Ramos | Characteristics and competition for nest cavities in burrowing Procellariiformes[END_REF].

In seasonal seabirds, the date of arrival at the breeding grounds and the laying date tend to vary among species due to exogenous (photoperiod) and endogenous factors (e.g., individual hormonal status, circadian rhythm) that elicit migratory and breeding behavior, and/or to differences in feeding ecology [START_REF] Both | Adjustment to climate change is constrained by arrival date in a long distance migrant bird[END_REF][START_REF] Le Corre | Breeding seasons of seabirds at Europa Island (southern Mozambique Channel) in relation to seasonal changes in the marine environment[END_REF][START_REF] Brooke | Albatrosses and petrels across the world[END_REF][START_REF] Lehikoinen | Arrival and departure dates[END_REF]. Early breeding is generally advantageous in terms of breeding success [START_REF] Nelson | Seabirds. Their biology and ecology[END_REF][START_REF] Daan | Food supply, and the annual timing of avian reproduction[END_REF]; see also Ollason and Dunnet, 1988;[START_REF] Barba | The cost of being late: consequences of delaying great tit Parus major first clutches[END_REF][START_REF] Sydeman | Repeatability in egg-laying date and its relationship to individual quality for common murres[END_REF]. However, if the breeding locality harbors a predatory species that faces a food shortage during the period when birds are absent, the earliest-arriving individuals are also the most likely to suffer mortality due to predation. The critical question here is: can predation counterbalance the cost of arriving later at the breeding grounds?

To address this question, insular seabird species represent especially suitable models. On most oceanic islands, seabirds have evolved without terrestrial mammalian predators until recently, when rats (Rattus spp.) and cats (Felis silvestris catus) were introduced by humans on several islands [START_REF] Atkinson | The spread of commensal species of Rattus rattus to oceanic islands and their effects on islands avifaunas[END_REF]Johnstone, 1985;[START_REF] Veitch | Methods of eradicating feral cats from offshore islands in New Zealand[END_REF]. Many seabird species lack the behavioral and ecological adaptations that would enable them to cope successfully with mammalian predators [START_REF] Lack | Ecological adaptations for breeding in birds[END_REF][START_REF] Warham | The Petrels. Their Ecology and Breeding Systems[END_REF]. Consequently, the impact of introduced predators on insular seabird populations has been catastrophic in most cases [START_REF] Atkinson | The spread of commensal species of Rattus rattus to oceanic islands and their effects on islands avifaunas[END_REF][START_REF] Veitch | Methods of eradicating feral cats from offshore islands in New Zealand[END_REF][START_REF] Pontier | The diet of feral cats (Felis catus L.) at five sites on the Grande Terre, Kerguelen archipelago[END_REF]Blackburn et al., 2000). [START_REF] Pontier | Limited nest site availability helps seabirds to survive cat predation on islands[END_REF] studied certain aspects of competition for nesting sites in a seabird species that faces predation from cats. They concluded that, surprisingly, limited nest site availability could favor the long-term persistence of the seabird population by creating a large pool of non-breeding birds that can buffer the demographic impacts of factors such as bad climatic conditions on land. However, their model was a predator-prey model that included only one prey species and prey breeding limitation. The potential existence of several species competing for nest sites was neglected. The present paper aims to determine whether and how the outcome of this competition is affected by predation.

There are several mechanisms through which predators can alter the strength and direction of competition between prey species [START_REF] Chase | The interaction between predation and competition: a review and synthesis[END_REF]. It is widely acknowledged that alien predators are a major factor in biodiversity loss [START_REF] Courchamp | Mammal invaders on islands: impact, control and control impact[END_REF]. Indeed, the first direct effect of predation is a reduced abundance of native prey and hence an increased risk of extinction. Moreover, predation can generate indirect competition between two otherwise independent prey species, which can potentially lead to the extinction of one of the two prey species [START_REF] Courchamp | Cats protecting birds: modelling the mesopredator release effect[END_REF]. This is because increasing the abundance of one prey species leads to an increase in predator numbers and hence a decline in the other prey population. However, some mechanisms may allow predation to promote coexistence between prey species. This is the case, for example, if prey that are the best competitors for resources are the most vulnerable to predation [START_REF] Armstrong | Prey species replacement along a gradient of nutrient enrichment: a graphical approach[END_REF][START_REF] Abrams | Is predator mediated coexistence possible in unstable systems?[END_REF][START_REF] Leibold | A graphical model of keystone predators in food webs: trophic regulation of abundance, incidence, and diversity patterns in communities[END_REF], when different prey species occupy different shelters to avoid predation [START_REF] Jeffries | Enemy free space and the structure of ecological communities[END_REF][START_REF] Holt | The ecological consequences of shared natural enemies[END_REF] or when the intensity of predation depends on prey density [START_REF] Roughgarden | Species packing and predation pressure[END_REF][START_REF] Gendron | Models and mechanisms of frequency-dependent predation[END_REF][START_REF] Huntly | Herbivores and the dynamics of communities and ecosystems[END_REF].

A c c e p t e d m a n u s c r i p t 5

To investigate how predation by introduced cats (hereafter referred to as predation) can modify the benefit-cost balance of arriving early at the nesting sites and hence alter seabird community structure, we built a mathematical model considering two seabird species that differ only in their date of arrival on a hypothetical remote island. These species both face predation and share the same nesting sites. One fundamental model assumption is that the impact of cat predation may differ between seabird species according to their date of arrival.

Indeed, early-arriving birds arrive before a surge in the rabbit population and therefore constitute the main prey of cats during this period. Late-arriving birds suffer weaker predation because they return to the island at the moment when rabbits become abundant and are again an important target for cats. Here we determine whether predation can help late-arriving birds -which here are always disadvantaged in the absence of predation -to obtain nest sites and to breed as successfully as their early-arriving counterparts.

Materials and methods

The mathematical model

Our mathematical model extends classical Lotka-Volterra Competition equations (see [START_REF] Murray | Mathematical Biology, I, An introduction[END_REF], for a review). It is parameterized to represent two typical colonial burrownesting seabird species on an island (or a group of islands) that is home to both cats and rabbits, as in the Kerguelen archipelago, southern Indian ocean [START_REF] Pontier | The diet of feral cats (Felis catus L.) at five sites on the Grande Terre, Kerguelen archipelago[END_REF], or on the Canary Islands, subtropical north-eastern Atlantic [START_REF] Nogales | Trophic ecology of feral cats (Felis silvestris f. catus) in the main environments of an oceanic archipelago (Canary Islands): an updated approach[END_REF]. The first species of birds breeds early (early breeders, species 1), while the second species starts breeding later (late breeders, species 2). In our model, superscript labels 1 and 2 represent early and late breeders, respectively. The two seabird species are assumed to be otherwise identical. Given this framework, we can be sure that the outcome of the competition between

A c c e p t e d m a n u s c r i p t

the two seabird species will be the result of the selective advantage and disadvantage conferred by their dates of arrival on the island.

Our model is a simplified version of that proposed by [START_REF] Pontier | Limited nest site availability helps seabirds to survive cat predation on islands[END_REF]. We consider two seabird species with a balanced sex ratio, such that the model only represents the changes in the number of females. The birds' life cycle is illustrated in Figure 1. We use K n to denote the number of available nesting sites on the island, with B n (t) being the number of nests occupied at time t. To simplify, we assume that all the birds occupying a nest behave in the same manner: all birds leave the colony at the same time at the end of the breeding season, and if one individual in a nest dies, then all the individuals from this nest will die. Given the extended incubation period in seabirds (between 18 and 83 days, depending on the species; see Appendix 2 in Schreiber and Burger, 2002), the bulk of predation occurs before the eggs hatch (especially in the early-arriving species) and hence mainly affects adults. This pattern results in a very high rate of breeding failure: without biparental care, chicks die along with their parents (see [START_REF] Lack | Ecological adaptations for breeding in birds[END_REF].

At time t 1 (t 2 ), all the individuals of species 1 (species 2) leave the nest, leading to a number bB n 1 (bB n 2 ) of immature individuals, where b is the average number of juveniles in each occupied nest. The 'immature' class (B i ) includes all individuals between fledging and the age when they will become socially mature (compartment B m ) at a rate J 1 . All the birds that have returned to the colony at least once since fledging and the birds that will return ashore for the first time in their lives during the current breeding season are considered 'socially mature'. Socially mature birds become prospectors at a rate J 2 1 (t) for early breeders two seabird species as modeled here is represented in Figure 2), prospecting birds start colonizing vacant nests (at a rate P 1 (t) for early breeders and P 2 (t) for late breeders). All the birds face a natural mortality (i.e., mortality due to any cause other than predation) at rate m.

We introduce a saturating term to model the rate at which socially mature birds become prospectors: we assume that the number of breeding and prospecting birds is limited to a certain quantity, K b , due to limited resources at sea. Indeed, the distribution and abundance of marine organisms [START_REF] Waluda | Influence of oceanographic variability on recruitment in the Ilex argentines Cephalopoda: Ommastrephidae fishery in the South Atlantic[END_REF], linked to variations in oceanographic conditions (e.g., [START_REF] Deacon | Seasonal variations in the water temperature and salinity near South Georgia 1925-1937[END_REF], can directly influence individuals' body reserves, their breeding performance, their age at sexual maturity, adult survival rates, colony attendance and the proportion of breeding adults [START_REF] Drent | The prudent parent: energetic adjustment in avian breeding[END_REF]Erikstad et al., 1998;[START_REF] Weimerskirch | Seabird demography and its relationships with the marine environment[END_REF][START_REF] Inchausti | Inter-annual variability in the breeding performance of seabirds in relation to oceanographic anomalies that affect the Crozet and the Kerguelen sectors of the Southern ocean[END_REF][START_REF] Sandvik | Seabird life histories and climatic fluctuations: a phylogenetic-comparative time series analysis of North Atlantic seabirds[END_REF].

Our main simplification is that we do not model the dynamics of the cat population explicitly. This is a justifiable simplification since here we investigate how a varying (timedependent) predation pressure will influence the outcome of the competition between bird species. Not considering the dynamics of cats explicitly offers two advantages. First, we can easily control the time-dependence of the level of predation exerted on birds -much more easily than when predation pressure arises from complex dynamic interactions between birds, cats and their alternative preys. Second, it allows for easy extensions of the model. Here, predation is simply represented by a time-dependent increase in the mortality rate of nesting birds. It can easily be replaced by any factor that causes time-dependent additional mortality for nesting birds. For example, the conclusions of the model can be extended to situations where a seasonal disease would only affect nesting birds.

To simplify, the time-dependent mortality rate due to predation is chosen independent of the number of birds in the population. Only the birds occupying nests suffer predation. P(t)

A c c e p t e d m a n u s c r i p t

denotes the time-dependent mortality rate of birds as a result of predation, i.e., the rate at which occupied nests become vacant due to predation.

The model reads:

If t z t 1 :
and if t z t 2 :

Since all the breeding birds and juveniles of each bird species leave the island at the same time at the end of the breeding season (at t = t 1 for early breeders and t = t 2 for late breeders;

breeding adults return to the 'socially mature' class), we also have the following constraints:

Model parameters

The model time unit is the year. Whenever possible, we use basic values consistent with the parameters proposed by [START_REF] Pontier | Limited nest site availability helps seabirds to survive cat predation on islands[END_REF]. The rate at which birds become socially mature is J 1 = 0.25 year -1 . The maximum number of birds in breeding condition (K b ), that is, physiologically able to breed, is chosen equal to 10 5 birds, and we assume that there are 10 4 nesting sites on the island. Bird hatching and mortality rates are b=0.5 and m = 0.09 year -1 , corresponding to an annual adult survival rate of e 0.09 0.91.

Here seasonal rates are modeled as step functions (see also Figure The phenology of late breeders is chosen as a reference. The time elapsed between the arrival on land of early breeders and that of late breeders is given by ' B , i.e., the time during which species 1 suffers strong predation alone. During the strong predation phase, the mortality induced by predation involving the birds that occupy nests is P(t)=U and during the weak predation phase it is P(t)=UH The time lag between the arrival of the late breeders ashore and the end of the phase of strong predation is represented by ' P =t 2 -t 1 . H represents the ratio between the predation-induced mortality during the weak predation phase and that associated with the strong predation phase. Note that the impact of these parameters is often tested and hence they have no basic value. Values of P 0 and J 0 are assumed to have mean temporal values equal to those suggested by [START_REF] Pontier | Limited nest site availability helps seabirds to survive cat predation on islands[END_REF], leading to P 0 =76.39 year -1 and J 0 =12.73 year -1 . Finally, the basic values for the time lags are set to ' B =1 month and ' P =0, so that only late breeders occupy nests during the strong predation pressure period.

Results

Competition between seabird species without predation

First, we perform a quick analysis of the model where the predation term is set to 0 -i.e., U=0. We focus on competition between the two bird species (for the effect of the number of nests on the distribution of birds within classes, see [START_REF] Pontier | Limited nest site availability helps seabirds to survive cat predation on islands[END_REF].

The two species differ only in their breeding phenology. As a consequence, without predation and with all else being equal, the demographic trends of each species will be directly related to its reproductive success. Given this fact, early arrival permits early breeders to monopolize nests, affording them an important evolutionary advantage over their competitors. In other words, the competition is always won by the early breeders. Figure 3 illustrates the general behavior of the system: whatever the initial conditions, late breeders go extinct while early breeders thrive. To assess the importance of the model parameters in terms of the outcome of the competition between the two bird species, we define four regimes in which the system can fall. To do this, we start from an initial state where early breeders are at the predation-free equilibrium and the number of birds in each class of the model in late breeders is equal to 1% of the number of birds in the same class in early breeders. We consider a species to be persistent at the ecological scale when its total numbers after 200 years are at least equal to the initial (i.e., time 0) total number of late breeders. This gives a good idea of the outcome of the competition between the two seabird species at an ecological scale.

We define the 'late breeders' and 'early breeders' regimes as being those in which only late breeders or only early breeders, respectively, persist after 200 years. We define as the First, we consider the basic values of the parameters and determine the impact of the maximum predation pressure (U) and the relative predation pressure between the weak and strong predation periods (H). Since ' p =0, late breeders do not suffer any predation when H=0.

They are favored when the predation pressure -exerted only on their competitors -is strong (Figure 5a). Under lower predation pressures, the two seabird species coexist, but only for a restricted range of U. The selective advantage of late breeders rapidly decreases as H increases.

Although strong predation levels are required to balance the selective advantage conferred by early breeding, for H >0.45 even late breeders cannot cope with the predation-induced mortality. In other words, seasonal variations in predation pressure must be significant to generate an environment where late breeders coexist with early breeders or are favored.

Next we investigate the effect of the other nine parameters. Here we only present the results obtained for the time lag between the arrival of the two species at the colony site (' B )

and between the arrival of late breeders and the end of the strong predation phase (' P ), which are the most important for the outcome of the competition. Results obtained using the seven remaining parameters are presented in the electronic supplementary material. To determine realistic time lag values that are compatible with the coexistence of both species or with a reverse outcome of the competition between the two bird species, we need to understand how the main model parameters impact competition. Therefore, we set H=0.1, a value that allows both coexistence, selection of early or late breeders and the extinction of both species, depending on the value of U (Figure 5a). U is variable in all figures.

The most important factor in terms of the persistence of late breeders -alone or coexisting with early breeders -is the time lag between the arrival at the colony of the two bird species (' B ) (Figure 5b). Short time lags clearly favor early breeders, which have time to colonize a large number of nests without being at significant risk of predation. As a result, late breeders cannot persist when the time lag is shorter than one week. Above this threshold, we can see that as the time lag increases, the long-term persistence of late breeders is apparent for a broader range of values of U. This is because arriving earlier does not give early breeders a greater chance to breed, but it rather exposes them to longer sustained predation pressure. In that sense, increasing ' B is similar to increasing H while keeping UH constant.

Figure 5c shows that short predation time lags (' P ) favor the long-term persistence of late breeders. This can be explained by the fact that if the intense predation phase lasts over a long period when late breeders are nesting, then the differential in the predation pressure suffered by the two species will tend to be minimized. Moreover, longer time lags lead to all of the birds being more strongly affected by predation and this in turn will decrease the value of the predation coefficient (U), above which both species may go extinct.

Discussion

Studying the impact of introduced predators is of great importance for the conservation of seabirds on sub-Antarctic, tropical and temperate islands where the native avifauna exhibits high levels of endemism and trophic webs are simplified. However, the problem of seabird population management cannot be regarded as a simple prey-predator interaction, where decreasing predator population size would lead to a straightforward growth in the prey population. For example, theoretical [START_REF] Courchamp | Cats protecting birds: modelling the mesopredator release effect[END_REF] and empirical [START_REF] Palomares | Interspecific killing among mammalian carnivores[END_REF] evidence have shown that removing a top predator can lead to an increase in a mesopredator population and, surprisingly, to an eventual decrease in the prey population when the mesopredator also preys on the prey (a phenomenon known as the 'mesopredator release effect'). In such a context, models represent useful tools that can offer important

A c c e p t e d m a n u s c r i p t

insights into the mechanisms involved [START_REF] Courchamp | Rabbits killing birds: modelling the hyperpredation process[END_REF]Gaucel et al., 2005;Gaucel and Pontier, 2005;[START_REF] Zhang | Rabbits killing birds revisited[END_REF].

Here we determine whether and how the presence of a predator, combined with competition for nesting sites, may affect the seabird community structure, either by favoring long-term coexistence between late-and early-arriving seabird species or by reversing the outcome of competition by favoring late breeders. Considering two species that differ only in terms of their date of arrival on the island, we showed that, in the absence of a top predator, competition for nests ends up pushing the later-arriving species to extinction. Such a situation might occur in the near future with, for example, the Bulwer's petrels Bulweria bulwerii from the Azores (northern subtropical Atlantic), which face strong competition for burrows with the larger Cory's shearwaters Calonectris diomedea [START_REF] Ramos | Characteristics and competition for nest cavities in burrowing Procellariiformes[END_REF][START_REF] Bried | Which future for Bulwer's petrel in the Azores? Airo 15[END_REF].

The presence of cats alters the outcome of competition between the two species, provided that the predation pressure faced by nesting seabirds exhibits large seasonal variations. The over-predation suffered by the early-arriving birds counterbalances (and sometimes offsets) the benefits of their early nest monopolization. As a result, this permits coexistence between the two bird species or even the competitive exclusion of early-arriving birds. To test model predictions, it would be interesting to compare the relative distribution of species having different dates of arrival in areas with and without cat predation. The Kerguelen archipelago is especially suitable for studying this question, since it includes islands with and without cats.

However, it is obvious that the model presented here is more general and may be equally valid for seabird species that breed on other oceanic islands where mammalian predators have been introduced.

One fundamental model parameter is the magnitude of seasonal fluctuations in cat predation pressure. Even though early-arriving birds suffer from stronger predation than late-

A c c e p t e d m a n u s c r i p t

arriving ones, strong predation only occurs during a short period, and strong predation pressure is essential to counterbalance the huge advantage conferred by early nest monopolization. However, if this pressure is also strong for late-arriving birds, both species will go extinct. As a result, the long-term persistence of late-arriving birds is apparent only when the differential in predation pressure is very large. It is also interesting to note that the optimal date of arrival for one species depends on the strategy adopted by the other. Arriving at a time t can be advantageous when the other species arrive at time t+H, but disadvantageous when other individuals arrive at time t+2H. This is because a small differential in the date of arrival is sufficient to monopolize nesting sites. A larger differential mainly leads to a longer period of strong predation without providing important advantages for reproduction.

Considering the effects of other model parameters as well as the values of the parameters chosen (the latter were favored considering the seabird populations from the Kerguelen archipelago), we estimate that the ratio of predation pressures between the strong and weak predation phases must be at least 1/H=2 to ensure the long-term persistence of late-arriving birds. It is challenging to determine whether this is realistic in the field, but considering that rabbit densities can become extremely high in summer, a differential of 2 in the pressure between high and low predation phases seems plausible.

Our model, of course, simplifies a complex system. Several aspects of the system have been neglected to make the model more readable. In particular, we assumed that the two seabird species behaved identically except for their arrival date at the colony. The date at which seabird species come ashore to breed is conditioned by the phenology of their prey (see Introduction As argued previously, the model can be used to take account of any factor that may lead to an additional seasonal mortality of breeding individuals. One of these factors may be parasitism. First, parasitism is often seasonal and more likely to occur on islands where bird densities can be very high. Second, many parasites can induce very strong additional mortality to their hosts (see, for example, the recent outbreak of avian cholera in Amsterdam albatrosses Diomedea amsterdamensis; [START_REF] Weimerskirch | Diseases threaten Southern Ocean albatrosses[END_REF].

Beyond inter-species competition, several works have shown that phenology is a fundamental trait for intra-species competition (in plants, [START_REF] Harris | Root phenology as a factor of competition among grass seedlings[END_REF]; but also in mammals, [START_REF] Mysterud | The timing of male reproductive effort relative to female ovulation in a capital breeder[END_REF]and insects, Frederickson, 2006). Even though the mechanisms studied here concern inter-species competition, they can also extend to situations where intra-species competition occurs [START_REF] Rowan | Regulation of sea-bird numbers[END_REF][START_REF] Ramos | Characteristics and competition for nest cavities in burrowing Procellariiformes[END_REF], with the latest-arriving individuals failing to obtain a nest. Indeed, the date at which individuals arrive at their breeding localities can represent a heritable trait in some bird species [START_REF] Brown | Weather-mediated natural selection on arrival time in cliff swallows (Pterochelidon pyrrhonota)[END_REF][START_REF] Møller | Heritability of arrival date in a migratory bird[END_REF] but see [START_REF] Potti | Arrival time from spring migration in male pied flycatchers: individual consistency and familial resemblance[END_REF]. In this case, the argument that early-arriving species suffer higher mortality would be enhanced by the fact that, within a given species, arriving earlier than the optimal date of arrival (without predation) is costly (either in terms of parental or of chick mortality).

  for late breeders. Prospectors (class B p ) are those individuals that come ashore during the current breeding season. This class includes both former breeders that are ready to breed again and individuals that are now ready to breed for the first time. During the appropriate period of the year that depends on seabird species (the seasonal behavior of the

  Effect of predation on inter-species competition for nestsSince predation is most severe at the time when early breeders arrive at the colony, early breeders experience increased mortality. This results in an increasing number of vacant nests, which may then be available to late breeders. Do increased mortality and the turn-over in nests induced by predation balance the selective advantage of nest monopolization conferred by early breeding?Our results show that the response to this problem depends on many factors, mainly the predation pressure. Unsurprisingly, under weak predation pressures, early breeders are always favored (Figure4a, U=0.5). Strong predation pressures tend to favor late breeders (Figure4b, U=1.5), but if predation is too strong both species go extinct (Figure4c, U=3). Asymptotic coexistence, where the two species coexist in a stable cyclic state, is apparent in our model but only for restricted ranges of the parameters. Temporary coexistence (Figure4d, U=1)i.e., coexistence during an ecologically long period of time (up to several hundred years) -is apparent for a broader range of values.

  regime the situation for which both seabird species are persistent after 200 years. We define as the 'extinction' regime the regime under which both species have disappeared after 200 years.

  same colony, even in the absence of predation. The model clarifies how, even though predation may not account for all coexistence between early-and late-arriving species, it can still constitute an important force that may favor coexistence under realistic circumstances.

Figure 1 .

 1 Figure captions

Figure 2 .

 2 Figure 2. Seasonal variations in seabird behavior and predation pressures.

Figure 3 .

 3 Figure 3. Competition between early and late breeders in the absence of predation. In

Figure 4 .

 4 Figure 4. Typical evolution of competition between early (solid line) and late (dotted

Figure 5 .

 5 Figure 5. Impact of the model parameters on the regime under which the system falls

  ). A species arriving at a given date one year may arrive slightly earlier or later the next year. Furthermore, species are never strictly identical, and other fitness constraints

(such as physiological constraints) may result in additional costs related to early breeding. All of these factors, not modeled here, may explain why early-and late-arriving species can

Acknowledgments

This work was supported by IPEV ("Popchat" n°279) and the "Environment & Sustainability" Department of CNRS ("Zone Atelier de Recherche sur l'Environnement Antarctique et


Keywords: Time-reversal, EMC, Powerline communications

Power Line Communication (PLC) is a technique used to deliver information over the electrical networks. The capacity and performance of PLC has evolved, over the past few decades, from very low bit rate power grid telemetry applications to inhome broadband internet services. However, there are serious electromagnetic compatibility (EMC) issues between PLC systems and radio broadcasters. Due to their dispersive nature, the PLC channels offer a rich scattering medium to a signal. Time-reversal (TR) is a technique which exploits scattering to obtain two major advantages: an improved signal to noise ratio (SNR) at the receiver, and reduced radio pollution to improve the EMC scenario.

I. INTRODUCTION

Power Line Communication (PLC) is a technique for carrying information over the conductors which are primarily designed and installed for electrical power transmission. Electrical power is transmitted over high voltage transmission lines, distributed over medium voltage and used inside buildings at lower voltages. Power line communications can be applied at each stage for various applications. The inhome PLC, operating in 2-30 MHz band and planned to be enhanced to higher frequencies up to several hundreds of MHz, is experiencing serious EMC issues with existing radio broadcasters such as amateur radio and FM radio [START_REF] Brice | Restrictions related to the electromagnetic compatibility emission issue in power line communications[END_REF]. The high bit rate PLC systems, using orthogonal frequency division multiplexing (OFDM), are suffering from throughput loss due to EMC constraints [START_REF] Brice | Restrictions related to the electromagnetic compatibility emission issue in power line communications[END_REF]. Lack of a unanimous network topology, branching, load mismatch and non standard network installation are some factors due to which the PLC channel exhibits rich scattering and multipath for high bit rate signals, particularly for inhome applications [START_REF] Zimmermann | A multipath model for powerline channel[END_REF]. On the other hand, in the field of wireless communications, time-reversal (TR) is a well-known technique used to exploit the multi-paths in a richly scattering medium or channel for SNR enhancement at the receiver along with improved EMC. This technique was developed in the field of acoustics and under water marine communication. It has been recently applied to the field of wireless communications [START_REF] Geoffroy | Retournement temporel d'ondes electromamgnetique et application à la télécommunicati-on en milieux complexes[END_REF].

II. TIME-REVERSAL

The general concept of TR is a two step process. In the first step called channel estimation, a short training pulse ) (t x as shown in figure 1 (a), is emitted by a source s and a signal ) (t y n is received at corresponding n elements of an array. In the second step, as shown in figure 1 (b), called information transmission, each array element emits information pre-filtered by a corresponding time-reversal filter ) ( t y n -. As a result, a signal well focused in space and tightly compressed in time is received at the source s. Figure 1 presents these different steps.

(a) (b) Figure 1: Two steps of a Time-Reversal experiment in radio communication [START_REF] Kyritsi | PhD class on Adaptive Antennas[END_REF] The physical aspects of time-reversal are quite straight forward to demonstrate. Electromagnetic wave fronts, emitted by a source, which travel through a rich scattering medium experience individual delays depending on the impulse response of the medium. When the time-reversed version of these wave fronts is injected into the same medium, they trace their way back to focus on the point of emission.

More specifically, from a digital communication point of view, the application of time-reversal requires the knowledge of the Channel Impulse Response (CIR) h(t) at the transmitter, which is the purpose of the channel estimation stage. The signal to be transmitted, s(t), is first pre-processed using a filter with impulse response h*(-t), where * represents the complex conjugation. The received signal r(t) is the convolution of the pre-processed transmitted signal with the

Time-Reversal for EMC improvement in Powerline Communications

Rehan Hashmat (1) , Pascal Pagani (1) , Ahmed Zeddam (1) , Thierry Chonavel (2) (1) Orange Labs, 2 av. Pierre Marzin, 22300 Lannion, France rehan.hashmat@orange-ftgroup.com, pascal.pagani@orange-ftgroup.com, ahmed.zeddam@orange-ftgroup.com (2) Telecom Bretagne, CS 83818, Technopôle Brest Iroise, 29238 Brest Cedex, France e-mail: thierry.chonavel@telecom-bretagne.eu CIR, as follows:

r(t) = s(t) ⊗ h*(-t) ⊗ h(t) (1)
where ⊗ denotes the convolution operator. By denoting R(f), S(f) and H(f) the frequency spectrums of the received signal, transmitted signal and channel transfer function (CTF) respectively, Eq. ( 1) can be reformulated as

R(f) = S(f) x H*(f) x H(f) = S(f) x |H(f)|² (2)
In the field of wireless communications, it has been demonstrated that the time-reversal technique offers a certain power gain at the receiver [START_REF] Pajusco | On the use of uniform circular arrays for characterizing UWB Time Reversal[END_REF]. The pre-processing filter should be normalized to a unit power and can be obtained as

D(f) = H*(f) / (E[ |H(f)| 2 ] ) 1/2 (3)
where * represents the complex conjugate, and E[.] represents the expectation (or mean) function. Figure 2 shows the functioning of TR technique at block level. The existing PLC systems work in 2-30 MHz range and employ a multi-carrier modulation, such as OFDM, for data transmission. An up gradation of PLC band up to 100 MHz has been proposed within the ICT OMEGA project [START_REF]7th Framework Programme: ICT-213311 OMEGA, D3.2[END_REF], and higher frequencies are investigated in the industry. Since PLC networks comprise of unshielded wires, they are a source as well as a victim of electromagnetic interference. Therefore, serious EMC issues have emerged between PLC systems and existing radio broadcasters such as amateur radio and FM radio etc. Figure 3. Local FM radio received on PLC network at Orange Labs, Lannion [START_REF] Brice | Restrictions related to the electromagnetic compatibility emission issue in power line communications[END_REF] Some solutions have been proposed to mitigate the EMC issues. These solutions, in general, comprise of non-adaptive notching of some of the OFDM carriers and thus degrade the data throughput of PLC systems. Few efforts have been made to obtain adaptive and intelligent carrier notching through radio cognitive techniques [START_REF] Brice | Restrictions related to the electromagnetic compatibility emission issue in power line communications[END_REF].

IV. TIME-REVERSAL FOR PLC

When applying TR specifically to a PLC network, the level of unintentional radiated power will decrease. This represents an inventive way of solving the EMC issue linked with powerline communications.

To understand this phenomenon, some insights of the mechanisms of electromagnetic waves radiated from a transmission line need to be clarified. When transmitting a signal on a transmission line, the network topology and the connected loads (i.e. boundary conditions) induce a given distribution of current along the transmission line. From this current distribution, each infinitesimal section of the transmission line can be considered as an elementary, independent, radiating source, where the amount of radiated power is linked to the intensity of the current at this location. In addition, it should be noted that the improved SNR at the receiver contributed by TR technique can in turn allow lower power levels at the transmitter. This is particularly beneficial for PLC systems which are suffering from severe transmit power regulations.

A. PLC Channel Measurements

An extensive inhome PLC channel transfer function measurement campaign was launched by Orange Labs in several houses at Lannion. In total 144 real-life PLC channels were measured up to 100 MHz and grouped in nine classes according to mean channel attenuation [START_REF] Tlich | Indoor Power-Line Communications Channel characterization Up to 100 MHz-Part I: One-Parameter Deterministic Model IEEE Transactions on Power Delivery[END_REF]. Figure 5 shows that there is a considerable amount of variability of channel attenuation. For example, class 1 channels offer attenuation less than 10 dB up to 70 MHz while class 9 channels exhibit an attenuation of around 53 dB in the same band. It should be noted that the middle classes 4, 5, 6 and 7 contain most channels.

B. Time-Reversal Performance Parameters

We defined two performance parameters for the evaluation of TR technique: Focusing Gain and Isolation Margin.

Focusing Gain

For illustration, consider the example of figure 4 which consists of three CTFs H ab , H ac and H ad . To obtain the Focusing Gain, we apply TR on each CTF individually, as shown in figure 2. Then, we shift to time-domain by inverse fast Fourier transform (IFFT). Focusing Gain is defined as the difference in dB between the peaks of the CIR before and after TR. The Isolation Margin is defined as the difference between the diagonal entry and the highest off-diagonal entry for a column in figure 7(b).

Isolation Margin = CTF kk, after TR -max (CTF nk,after TR ) (4)

The column-wise analysis is more correct and meaningful as it treats a given CTF k with n pre-processing filters, each normalized to unit power gain. The definition of Isolation Margin is illustrated graphically in figure 8. It has to be noted that for calculating the Isolation Margin we have taken into account the magnitudes at time t=0.

C. Data Processing and Results

We calculated Focusing Gain for 144 CTFs and the results are shown in the CDF of figure 9. We find that a Focusing Gain of 6 dB is available in 75% of inhome PLC channels. This is an interesting and encouraging result, not only for the signal reception but especially from the EMC point of view. The Focusing Gain obtained by Time-reversal technique can be translated into reduced transmit power of PLC systems, hence preventing them from becoming a source of unwanted emissions.

Figure 9. CDF of Focusing Gain for 144 CTFs

Figure 10 shows the plot between Focusing Gain and the peak value of CIR magnitude. It is quite obvious from this figure that the Focusing Gain generally increases for weaker PLC channels. Therefore, Time-reversal technique offers a healing effect to highly attenuated channels. This can be explained by the fact that attenuated channels generally offer rich multipath conditions, where the TR is more effective. The PLC systems are facing severe EMC issues of coexistence with amateur and commercial radio broadcasters. Such EMC problems may be solved by Time-Reversal technique. TR technique comprises of two steps: channel estimation and pre-filtering the information through TR filter before transmission. In this paper we defined two performance parameters: Focusing Gain and Isolation Margin. Then we evaluated these parameters for 144 real-life inhome PLC channels. The obtained results indicate that TR technique facilitates the PLC systems not to be source and victim of undesirable radio emissions, hence improving the PLC systems' electromagnetic compatibility.

Figure 2 .

 2 Figure 2. Block diagram of a TR communication system III. EMC ISSUES IN PLC

Figure 4 .

 4 Figure 4. A simplified PLC system

Figure 5 .

 5 Figure 5. Mean channel attenuation for a set of 144 measured CTFs divided into nine classes [7]

Figure 6 .

 6 Figure 6. Definition of Focusing Gain

Figure 7 (

 7 Figure 7(a). Block diagram of TR communication system with one transmit socket and multiple receive sockets

Figure 7

 7 Figure 7(b). Time-reversal implementation matrix for an ensemble of n CTFs.

Figure 8 .

 8 Figure 8. Definition of Isolation Margin

Figure 10 .

 10 Figure 10. Relationship between Focusing Gain and peak value of the CIR magnitude.

Figure 11

 11 Figure11shows the CDF of Isolation Margin for the group of 22 channels measured at the site no. 6. It demonstrates that almost 70% CTFs achieve an Isolation Margin of 6 dB. From the EMC point of view, Isolation Margin is an indicator of a reduction in interference level caused by a system to its ambience. Therefore, a PLC system with Time-reversal

Figure 11 .

 11 Figure 11. CDF of Isolation Margin for a group of 22 channels at site no. 6 V. CONCLUSIONS

Table 1

 1

	Site No. Tx Port	Number	Mean Isolation Margin
			of	(dB)
			Channels
	1	1	19	2.72
		2	6	13.27
		3	7	7.16
	2	1	6	5.66
		2	6	7.64
	3	1	13	3.58
		2	15	2.41
	4		34	3.48
	5		15	5.07
	6		22	6.95

summarizes the Isolation Margin values obtained at measurement sites.

Table 1 .

 1 Mean Isolation Margin


M N Chernodub
email: maxim.chernodub@lmpt.univ-tours.fr

Magnetic knots of deconfined CP-odd matter in heavy-ion collisions

We point out that metastable knots of deconfined hot quark matter may exist in the quark-gluon plasma due to local parity violating effects. These knots are stabilized by strong magnetic fields which induce electric currents via the chiral magnetic effect. The magnetic field in the knot resembles the spheromak plasma state which appears in the nuclear fusion devices. The size of the knot is inversely proportional to the chiral conductivity of the plasma, and the parity (P) and charge-parity (CP) symmetries are broken inside the knot. We argue that these knots may be created in noncentral heavy-ion collisions.

Magnetic knots of deconfined CP-odd matter in heavy-ion collisions Noncentral heavy-ion collisions may generate very strong magnetic field with the strength of the order of the hadronic scale. In LHC Pb-Pb collisions the strength of the magnetic field may reach the value eB max LHC 15 m 2 π , where m π ≈ 140 MeV is the pion mass [1]. A magnetic field of such strength should affect dynamics of the charged constituents of the quark-gluon plasma and consequently lead to several observable effects in heavy-ion collisions. For example, the quarkgluon plasma may contain parity-violating domains due to instanton and sphaleron transitions. In the parity-violating background the external magnetic field B leads to generation of a quark's electric current j via the so called chiral magnetic effect (CME) [2]:

j = σ χ B , (1)
where σ χ is the chiral electric conductivity which depends on properties of the quark-gluon plasma (the external electric field is assumed to be absent, E = 0). The first evidence of the existence of this exotic effect was recently reported by the STAR collaboration at the RHIC facility [3].

The transport law (1) leads to existence of certain nontrivial metastable states. A combination of Eq. ( 1) with the classical Maxwell equations provides us with the well known system of equations which plays an important role in usual (electromagnetic) plasma physics. Solutions of this system are usually called Chandrasekhar-Kendall states in astrophysical plasmas [4]. In the theory of nuclear fusion devices, the solutions are known as Taylor ("spheromak") states [5], which are the "natural-end configurations" in the plasma equilibrium. We suggest that due to the parity violating effects similar states may arise in the quark-gluon plasma created in heavy-ion collisions [6]. The spheromak state is a complicated compact structure of selflinked (knotted) magnetic lines. The simplest state (we call it as "knot") is a spherial solution of the finite radius R ∼ 1/σ χ . Typical lines of the magnetic field in these knots are illustrated in Figure 1. In heavy-ion collisions the knots may probably be formed in the parity-broken domains. Further details can be found in Ref. [6].

Figure 1 :

 1 Figure 1: Typical structures formed by the lines of the magnetic field (the illustration is from Ref. [6]).

This work was partially supported by the grant ANR-10-JCJC-0408 HYPERMAG.


Alexandre De Bernardinis
email: alexandre.de-bernardinis@inrets.fr

Denis Candusso
email: denis.candusso@inrets.fr

Fabien Harel
email: fabien.harel@inrets.fr

Xavier François
email: xavier.francois@utbm.fr

Gérard Coquery
email: gerard.coquery@inrets.fr

Experiments of a twenty cell PEFC operating under fault conditions with diode by-pass circuit for uninterrupted power delivery

Keywords: Polymer Electrolyte Fuel Cell, Multi-stack Fuel Cell, Fault tolerance, Degraded working modes, By-pass diode

The work presents the results of experiments related to the electrical and dynamical behaviour of a 500W, twenty cell Polymer Electrolyte Fuel Cell (PEFC) stack operated under fault condition and connected to an anti-parallel diode acting as a by-pass. The stack is placed in an experimental set-up that reproduces the electrical coupling in series of two fuel cells. The results allow the evaluation of the by-pass diode solution in the case of specific degraded working modes such as the break of the gas reactant feeding. The experiments presented in this article constitute an extrapolation and a complementary investigation of the preliminary results already achieved on a two cell PEFC stack and which had demonstrated the capability of the reverse diode to electrically isolate a fuel cell stack under fault. The proposed experiments focus on the dynamic behaviour of the stack under degraded working modes and point out the key-role of the fuel cell stack impedance in the triggering of the anti-parallel diode switching.

Introduction

Today for many energy conversion systems involving fuel cells (FCs) for stationary, transportation or even auxiliary power units (APU) applications, it becomes crucial and unavoidable to ensure a continuation of operation in case of a fault. It is essential to develop some technical concepts which permit degraded working modes and come to a fault tolerant fuel cell (FC) generator. Strengthen reliability, high power availability and power delivery continuation are fundamental for a vehicle (to reach the next station in case of a public transport) but also for stand-alone applications which need uninterrupted power delivery (hospitals, APU for emergency…) [START_REF] Corbo | Experimental analysis and management issues of a hydrogen fuel cell system for stationary and mobile application[END_REF][START_REF] Van Mierlo | Which energy source for road transport in the future? A comparison of battery, hybrid and fuel cell vehicles[END_REF]. Moreover the isolation of a FC stack under fault is important in order to protect its internal components which are very sensitive to degraded working situations. In the case of a Polymer Electrolyte Fuel Cell (PEFC) technology, the Membrane Electrode Assembly (MEA) can be subjected to different failures: membrane break, internal gas leakage, cell flooding or drying, poisoning of the catalysts areas...Redundancy and continuation of power delivery can be achieved through a multi-stack FC association when one FC stack remains out-of-work after a faulty operation [START_REF] Ozpineci | Integrating multiple Solid Oxide Fuel Cell Modules[END_REF][START_REF] Knights | Electrochemical fuel cell stack having a plurality of integrated voltage reversal protection diodes[END_REF][START_REF] Victor | System stack contingency and efficiency switching[END_REF]. A single stack (or group of cells) can be affected by several degradations during its operation, particularly when the power varies and consequently the amount of gas reactant. Some inhomogeneous gas distributions and induced local sub-stoichiometries (starvation phenomena) may also occur more frequently in larger stacks fed by fast gas flow changes. In some cases involving fast load variations, the coupling of FCs with additional buffer energy storage elements (super-capacitors, power batteries) is also required [START_REF] Paladini | Super-capacitors fuel-cell hybrid electric vehicle optimization and control strategy development[END_REF][START_REF] Uzunoglu | Dynamic modeling, design and simulation of a PEM fuel cell/ultracapacitor hybrid system for vehicular applications[END_REF]. A hybrid FC system is often considered for transportation applications in order to adapt the dynamical response of the FC generator to transient load phases and for energy saving during the braking phases of the vehicle [START_REF] Paladini | Super-capacitors fuel-cell hybrid electric vehicle optimization and control strategy development[END_REF][START_REF] Uzunoglu | Dynamic modeling, design and simulation of a PEM fuel cell/ultracapacitor hybrid system for vehicular applications[END_REF][START_REF] Mj | Power management and design optimization of fuel cell/battery hybrid vehicles[END_REF].

As an example of possible operating problem, let us consider the case of cells suffering from fuel starvation, which means that the cells are not fed with sufficient amounts of reactive gases.

Then, the cell voltages will drop down below a low threshold, which can be critical for the cell operation and performances and for their lifetime as well. In order to isolate and protect the stack one solution consists in monitoring the cell voltages and shutting down an affected stack if a critical low voltage is detected. Another complementary solution should consist in the use of reverse by-pass diodes electrically connected in anti-parallel to each FC stack or groups of cells.

These diodes can isolate the defective cells (or even an entire stack) and authorize the continuation of power delivery. This technique has already been used in the industrial sector to ensure the continuation of power delivery by hydrogen / oxygen FC stacks in a sub-marine [START_REF] Strasser | PEM Fuel Cell module for an air independent propulsion system in a submarine, Handbook of Fuel Cells -Chapter 88 H 2 /0 2[END_REF]. Some diodes can also be employed in order to protect either each individual cell or a group of cells within a stack. With the diodes allowing the deviation of the stack current, the cells are prevented against the possible adverse effect of low or reverse voltages. In the patents [START_REF] Knights | Electrochemical fuel cell stack having a plurality of integrated voltage reversal protection diodes[END_REF][START_REF] Victor | System stack contingency and efficiency switching[END_REF][START_REF] Strasser | PEM Fuel Cell module for an air independent propulsion system in a submarine, Handbook of Fuel Cells -Chapter 88 H 2 /0 2[END_REF][START_REF] Josef | Patents of SIEMENS AG: WO0245197 and DE10059392[END_REF], the authors describe some FC systems comprising a plurality of stack assemblies having their integrated diodes.

The solution of by-pass diodes used in case of a faulty stack has already been evaluated at the FC LAB laboratory in Belfort. Preliminary works have been conducted on a two cell PEFC stack [START_REF] Candusso | Fuel cell operation under degraded working modes and study of a diode by-pass circuit dedicated to multi-stack association[END_REF][START_REF] Coddet | Study of Proton Exchange Membrane Fuel Cell safety procedures in case of emergency shutdown[END_REF]. This first study is now extrapolated to a twenty cell PEFC stack. Experiments and test analyses through modelling are proposed in this article.

The article is organised as follow: First the problematic of power delivery continuation for multi-stack FCs using by-pass diodes is reminded. Secondly, a modelling and simulation approach permit to describe the behaviour of the FC stack under a specific degraded conditions.

The switching capability of the anti-parallel diode and the key-role of the FC internal resistance in the triggering of the diode conduction are pointed out. Then, experimental tests have been performed and the various results analysed. The twenty cell PEFC under test with its anti-parallel diode is respectively connected in series to a constant and adjustable DC voltage source (0-20V) which emulates a second FC. As a second experiment, the PEFC is connected in series to a 12V lead-acid battery to represent a hybrid power source. Some specific degraded working modes will be imposed to the FC stack alike the sudden interruption of the gas reactant feeding to the FC.

The aim is to observe and understand the behaviour of the PEFC stack under these degraded situations and to validate experimentally the role of the anti-parallel diode as a by-pass to the faulty stack. Current and power regulations are applied to the load during the tests. Let us remind that the work should be especially useful for electrical engineers and easily understandable by them since the models, simulations and tests presented in the paper are electrical engineering oriented.

Isolation of a FC stack under fault using a diode by-pass

As already mentioned in the introduction, an association of hydrogen / oxygen PEFC modules equipped with anti-parallel diodes has already been used in the case of an air independent propulsion system for submarine application [START_REF] Strasser | PEM Fuel Cell module for an air independent propulsion system in a submarine, Handbook of Fuel Cells -Chapter 88 H 2 /0 2[END_REF]. In the Submarine Class 212 from German Navy, eight 30-50kW PEFC modules are connected in series. If one of the FC modules fails, it is switched off, while the others continue to operate. Depending on the series connection of the FC modules, a diode connected between the electrical plugs of each module is necessary to ensure the current flow while one or more FC module(s) are out of operation. This principle of FC by-pass could be implemented in vehicles like electric buses, light rail vehicles (trams) taking into account the possible degraded working modes of the stacks linked to the constraints of the transportation environment.

The US patent publication [START_REF] Victor | System stack contingency and efficiency switching[END_REF] presents a switching system and control method implemented with a multi-stack FC system. The switching system enables FC stacks to be connected in series for providing power to load while removing the particular disadvantages of a series circuit. In the case of a stack fault, the faulty stack may be bypassed, whereby the remaining stacks provide power to the power user at a reduced capacity. The stack under fault is continuously monitored and is reintroduced to the series circuit if the fault clears. If the fault reoccurs once again "a predetermined number of times" after the stack has been reintroduced, a "reduced capacity" mode is initiated. Additionally, in the event of a reduced or an increased current demand, FC stacks are selectively switched in and out of the series connection, for limiting the overall operation voltage range of the FC stack system.

For the power supply of a DC network for on-board applications a possible solution should consist in using a power generator composed of n PEFC stacks connected in series (Fig. 1). This solution leads to an increase of the global input voltage and thus the voltage constraints on the load power converter are reduced as well as the current amplitude constraints for a given transmitted power. The FC multi-stack power generator is connected to a DC-DC power converter, which adapts the input voltage to the DC-Link voltage of the on-board electrical network. A battery imposes the DC bus potential and is also used for transient load power phases.

For simplification, each FC stack is represented in Fig. 1 as an ideal voltage source with a static resistance in series. Such an approach dealing with reliable operation involving protection by-pass diodes is also employed in photovoltaic (PV) generation systems. Some groups of ten to twenty PV cells connected in series to produce a reasonably high output voltage have an anti-parallel diode to ensure power delivery continuation in case of fault (mainly for partial lighting deficiency, a by-pass diode serves to decrease the effect of shadowing in the photovoltaic system while minimizing the power drops under shady conditions). The concerned references are mentioned in [START_REF] Karatepe | Voltage based power compensation system for photovoltaic generation system under partially shaded insolation conditions[END_REF][START_REF] Lasich | Bypass diode for photovoltaic cells[END_REF][START_REF] Balasubramanian | Photovoltaic cells integrated with bypass diode[END_REF][START_REF] Messenger | Photovoltaic Systems Engineering[END_REF][START_REF] Multon | Photovoltaic Generation, Lecture[END_REF][START_REF] Yoshioka | Non hot-spot PV module using solar cells with bypass diode function[END_REF].

Approach by simulation for a twenty cell PEFC stack

The simulation represents the electrical coupling of a twenty cell PEFC stack with its antiparallel diode (Diode AP) with a DC voltage source in order to simulate a twin-stack FC coupling. A contactor placed in series with the FC remains closed during the simulation. It is mainly used as a cut-off circuit for the stack protection or even is used to force a sudden circuit opening. Figure 2 shows the electrical circuit topology which was considered respectively for the simulation and following experiments described in section 4. The currents involved in the circuit are linked by Eq. ( 1) and the FC voltage is given by Eq. ( 2):

DiodeAP FC Load I I I   ( 1
)
FC m FC I R E U   (2)
The Diode AP technology is a Fast Recovery Epitaxial Diode (FRED). The conduction threshold of the Diode AP is V F = 2.2V (high voltage threshold for FRED diodes given at 25°C compared to other conventional diodes technologies).

Diode AP switching condition without the addition of Diode S2 in series with the FC

If the internal resistance of the contactor placed in series with the FC stack is neglected, the following relation Eq. ( 3) between the Diode AP voltage (V D_AK ) and the FC voltage (V FC ) is obtained:

FC m FC AK D I R E U V      _ (3)
When E equals zero or reaches values close to zero (during the starvation phase in particular), the FC behaves like a pure resistance (R m ) and the current in the FC stack is dependent both on the resistance R m and on the conducting threshold of the Diode AP (V F [V] diode forward voltage).

The current I FClim through the stack is limited by Eq. ( 4):

m F lim FC R V I  (4)
Then, the following relations corresponding to two different states can be considered:

 I Load ≤ I FClim :

With the addition of Diode S2 in series with the FC

The equation considering Diode S2 (voltage V DS2 ) added in series with the FC is:

2 _ 2 _ _ S D FC m S D FC AK D V I R E V U V        (5)
When the FC potential equals zero (E=0), taking into account the conduction threshold of Diode S2 (V FS2 ) and neglecting its series resistance in conduction, the FC current is limited by:

m FS2 F FClim R ) V (V I   (6)
If the value of the series resistance of Diode S2 (R FS2 ) is not considered as negligible regarding the resistance value of the FC (R m ), then the FC current is limited by:

) R (R ) V V ( I FS2 m FS2 F FClim    (7)
If the value of Diode S2 conduction threshold (V FS2 [V]) is equal to V F or higher, no current is passing through the FC electrical branch. The conduction thresholds of both diodes (Diode AP and Diode S2) impose the current amplitude in the FC branch during the switching.

Figures 3a and3b show simulation results performed for a 10A load current amplitude. In the first case (Fig. 3a) without the addition of Diode S2, the Diode AP does not conduct. The conduction threshold (V F ) of the Diode AP is not reached. For the second simulation (Fig. 3b) with additional Diode S2 connected in series with the FC stack, the same 10A load current amplitude is applied and the Diode AP is switched-on forced by the created voltage drop. The FC current is given by Eq. [START_REF] Uzunoglu | Dynamic modeling, design and simulation of a PEM fuel cell/ultracapacitor hybrid system for vehicular applications[END_REF]. The presented simulations demonstrate that the results can be very different depending on the FC stack resistance and load current. It should be noted that the conduction threshold of the Diode AP can be adjusted, either by choosing a suitable technology for the Diode AP (Schottky diodes having low threshold conduction, fast switching diodes…) or by associating more than one diode in series or in parallel. These simulation results will obviously be validated by a series of experiments but the first results provided in this section already show that the modelling tools developed can be very helpful to design elementary electrical topologies in order to better understand the diode switching phenomena and dynamic behaviour of the PEFC.

Experimental investigations on a twenty cell PEFC stack

The FC degraded working modes may have two main origins. The first cause is a possible inadequacy in the gas reactant supply to the stack or even a breakdown of the stack feeding in hydrogen and/or air. Thus, the voltages of the cells decrease dangerously and can lead to the starvation of several cells or to the starvation of the complete FC module [START_REF] Akira | Analysis of electrocatalyst degradation in PEMFC caused by cell reversal during fuel starvation[END_REF][START_REF] Zhixiang | Behavior of PEMFC in starvation[END_REF]. The second possible origin of a degraded working mode can be related with an electrical phenomenon such as a contactor switch-off or a short-circuit occurring in the power electronic interface.

Indeed, the shutting-down of a stack can occur following to one fault detection in the system. In both cases, the role of the anti-parallel diode is essential to ensure the current derivation and the electrical isolation of the faulty stack. In order to evaluate and characterise the electrical behaviour of the FC equipped with an anti-parallel diode, some degraded working modes have been imposed to a PEFC stack under test. Various experiments have been performed by the means of a specific set-up representing the coupling in series of two FC stacks (Fig. 2). The first FC is a twenty cell PEFC stack delivering a DC output voltage (UFC) which is the sum of the twenty single cell voltages. A variable 0-20V DC voltage source connected in series to the first stack simulates the second FC generator in operating condition. Another experiment will be conducted with the connection of an electrochemical lead-acid battery in series with the FC stack.

All the experiments have been carried out in order to characterise and evaluate precisely the "switching-on" of the by-pass diode (Diode AP) and simultaneously the dynamic behaviour of the PEFC stack to these transient fault operating situations. The experimental testing protocol for each experiment is described in the following subsections.

The experiments are realised using a 1kW in-house test bench developed in the FC Laboratory (FCLAB) in Belfort [START_REF] James | Association en parallèle de générateurs pile à combustible PEMFC (Parallel association of PEM fuel cells generators)[END_REF][START_REF] Harel Fabien | Expérimentations de piles à combustible en approche système embarqué (Experiments on fuel cells in embedded system approach)[END_REF]. The architecture of the test bench is specifically dedicated to the work on PEFC system integration aspects. The electrical and fluidic topologies of the test bench have been specially designed to study new concepts of flexible and modular structures for embedded FC systems. In comparison with a FC test stand allowing accurate FC stack characterisations, the test bench functionalities are simplified and the number of sensors is reduced. However, the main physical parameters of the FC stack can be measured and they can be controlled in order to manage the FC operating conditions efficiently and with sufficient accuracy to operate the FC properly. The load current can be imposed using an electronic load The electrical schematic set-up to perform the tests is reproduced in Fig. 5. One FC stack with its by-pass diode is connected in series with a DC source (either a 20V power source emulating another FC stack or a 12V lead-acid electrochemical battery).

First experiment: PEFC connected in series with a constant DC voltage supply

Let's refer to Fig. 5. The diode by-pass function (Diode AP) acts as a derivation circuit for the FC current. The electronic load imposes the load current amplitude. The Diode AP is an IXYS DSEI 2x61-10B (2x60A) Fast Recovery Epitaxial Diode (FRED) [START_REF]Data-sheet Fast Recovery Epitaxial Diode[END_REF] connected in anti-parallel to the PEFC stack under test. The package contains two independent diodes which are connected in parallel to constitute the anti-parallel Diode AP. FRED diodes have been selected because they have very short recovery times and offer low switching losses. They are often used as freewheeling diodes in power converters and for circuit protection like snubber diodes. Two diodes from a Semikron half bridge (IGBT/Diode module) SKM 75GB123D (1200V -75A) [START_REF]Data-sheet power IGBT/Diode module -SKM 75GB123D. SEMIKRON[END_REF] are connected in series with the PEFC; they constitute the Diode S2 used to impose a sufficient voltage drop which allows the switching of Diode AP for low voltages and current amplitudes which is the case in our tests. An on/off switch contactor is placed in series with the FC. A second one is positioned on the load circuit branch. Two sensors measure respectively the current in the two branches: LEM1 (current transducer type LA 50-S) is used for the FC current and LEM2 (type LA205-S) for the load current. The current passing through the Diode AP is deduced from both previous current measurements. The second FC in series is emulated by a Nemic-Lambda PWS (750-20) DC power supply which voltage ranges from 0 to 20V (in the same voltage range as the studied FC).

The picture in Fig. 6 shows the experimental test bench with the 500W twenty cell PEFC stack under test integrated in its experimental environment, the reverse Diode AP, the packaging with two diodes in series (Diode S2) with the PEFC and the DC power supply.

Test 2: Break in the air flow feeding the cathode and progressive switching of the

Diode AP for a 10A load current amplitude

A preliminary experiment has been initiated using only one of the two diodes (Diode S2) in series with the FC stack, but no conduction of the Diode AP was observed. Thus, the two diodes present in the packaging are connected in series to increase the voltage gap and allow the switching of the Diode AP.

The PEFC stack still operates in dead-end mode with purges. The load current is imposed at 10A level and controlled. The air compressor speed is 600 rpm, which corresponds to an air flow of 25 Nlmin -1 . The contactor in series with the FC stack remains closed during the experiment.

The air gas flow is voluntarily stopped by imposing a zero reference on the compressor (acting as an air flow regulator) so that the air pressure at stack inlet falls down to zero (Fig. 8a).

Simultaneously the load current continues to pass through the FC and the stack operates in abnormal condition with insufficient gas supply. The FC voltage decreases consequently to values close to zero Volts and when the Diode AP conduction threshold is reached, the Diode AP switches-on progressively. The dynamic response time of the Diode AP is within a couple of seconds (Fig. 8b). During the next constant phase, the FC power is 154W (15V; 10.3A) (Fig. 8b and8c). The cell voltages decrease to low values related with starvation phenomenon (Fig. 8d). To avoid such situation and any irreversible damage for the stack, the FC is fed again with air so that its global voltage increases rapidly. Another current switching between the PEFC and Diode AP is realised adopting the same test protocol: stop of the air gas flow by imposing a zero speed reference on the compressor. The air pressure at stack inlet falls to zero [mbar] and the Diode AP switching is achieved successfully.

Test 3: With a 15V DC voltage source and 25A load current amplitude

The voltage of the DC source is now set to constant 15V voltage amplitude. Test 3 is performed for a 25A load current amplitude. In this test the FC power reaches 320W (12.8V, 25A) during the steady-state phase. The power delivered by the DC voltage is 375W (15V, 25A) (Fig. 9b to Fig. 9d). The same operating mode is adopted. The Diode AP switches-on into conduction for a while. The current is shared between the Diode AP and the FC. The Diode AP current reaches around 22A, whereas the FC current reaches 3A during the commutation phase, The graphics in (Fig. 9e) and (Fig. 9f) show the evolution of the temperatures in the stack as well as minimal and maximal cell voltages during the test. The FC water temperature reaches a peak of 41°C before fault occurrence. At the end of Test 3, the FC impedance is measured at noload using the Agilent 4338B milliohm meter [START_REF]Agilent 4338[END_REF]. The measurement is realised after feeding the anode and cathode respectively with dry hydrogen and low humidified air in order to dry the membranes. The no-load voltage of the stack is 19V. The impedance of the twenty PEFC stack is in the range of 36 to 38mΩ at about 1.5 kHz. This value can be correlated with the resistance value (R m ) of the stack used for the simulation. Then the PEFC stack is fed normally with gas reactants and a current reference is imposed to the stack.

Second experiment: with a 12V Lead-acid battery connected in series with the PEFC

Nowadays, many studies dealing with the topic of electrical coupling between FCs and batteries and with power management strategies between the two devices are carried out [28]. In our study, the set made of the two electro-chemical sources can be considered as a low power twin-source hybrid system. Experimental results will be presented in the following section illustrating the electrical coupling of the 20 cell PEFC with a 12V electrochemical lead-acid battery connected in series.

The battery is a 12V / 4Ah valve regulated lead-acid battery (Yuasa NP4-12). The battery replaces the constant voltage supply used in the previous experiments. The internal resistance of the battery is equal to 40mΩ at 1 kHz. To simplify the scheme of the experimental set-up, the battery is represented in as an ideal 12V voltage source (Fig. 5.). At the beginning of the tests, the battery is fully charged to 12.4V.

Test 4: PEFC / 12V battery coupling and applying load current regulation

After a gradual step-up, the load current remains controlled at a 5A reference (Fig. 10b). Like for the previous experiments, the air flow is stopped to induce a break in the gas reactant feeding.

The FC voltage decreases and when the conduction threshold (V F ) of the Diode AP is reached, the progressive switching of the reverse diode can be observed. During the experiment the battery is discharged from 12.4V to 11V (Fig. 10c). The power delivered by the battery is around 60W (Fig. 10d).

Test 5: Power regulation strategy with the coupling PEFC and battery

In this test, the control strategy is modified and the load power is regulated. The power is established by successive power steps (Fig. 11d) until the value of 70W (reaching 30W on the battery and 40W on the PEFC). Then, the air gas flow is stopped and the switching of the Diode AP is progressively achieved (Fig. 11b). This last test illustrates the dynamic behaviours of both the PEFC and the lead-acid battery in response to a sudden load step. Both sources demonstrate their capabilities to react complementary to the current perturbation induced.

Conclusions

Several experimental tests have been performed in order to analyze the behaviour of a 500W twenty cell PEFC associated with an anti-parallel (reverse) diode (Diode AP) acting as a by-pass to the stack under fault. This technique has already been adopted by industrials for power applications involving multi-stack FCs. In a first approach, simulations have been performed on a twenty cell PEFC in order to better understand the switching mechanisms and dynamic behaviour of the twenty cell PEFC / Diode AP assembly. Then, various experimental tests were conducted.

The PEFC was firstly placed in a series electrical assembly connected to a DC voltage supply, which could emulate a second stack for instance and secondly with a lead-acid battery in order to simulate a hybrid twin-source coupling. The faults which were voluntarily caused on the PEFC stack were a sudden opening of the contactor in series with the FC stack and a break in the gas reactant feeding with a fast decrease of the FC voltage consequently. All the different tests have illustrated the possibility of stack isolation by the anti-parallel diode. However, the switching of the diode is not instantaneous; it depends on both the value of the internal impedance of the FC stack and the load current amplitude. In the experiments, it was therefore necessary to add diodes in series with the FC in order to increase the voltage threshold which leads to the conduction of the anti-parallel diode. The value of the internal resistance of the FC (high frequency resistance of the membrane) plays a key-role in the triggering of the diode conduction. Anyway the connection of an anti-parallel diode on the plugs of a FC has demonstrated to be a solution which allows operating the FC under degraded working modes and ensures a power delivery continuation in case of a faulty working of the FC.

Fig. 1 .

 1 Fig. 1. Possible simplified scheme for multi stack FC association equipped with anti-parallel by-

Fig. 2 .

 2 Fig. 2. Electrical circuit topology showing the PEFC, the Diode AP and all the devices used for

  Diode AP is blocked; I FC = I Load and I Diode AP = 0  I Load > I FClim : Diode AP is conducting; I FC = I FClim and I Diode AP = I Load -I FClim

Fig. 3 .

 3 Fig. 3. Simulation results for a 10A load current. (a) Diode AP blocked without additional Diode

(Fig. 4 .

 4 Fig. 4. Scheme of the FC test module used to investigate the behaviour of the twenty cell stack. T

Fig. 5 .

 5 Fig. 5. Electrical set-up reproducing the series coupling of two electrochemical power devices.

Fig. 6 . 4 . 1 . 1 .Fig. 7 .

 64117 Fig. 6. Picture of the test bench with the 20 cell PEFC in its experimental environment.

Fig. 8 .

 8 Fig. 8. Break in the air flow supply; Diode AP switching observed for 10A load current

Fig. 9 .

 9 Fig. 9. Diode AP switching for a 25A load current amplitude and 15V DC voltage supply. (a)

Fig. 10 .

 10 Fig. 10. Test with one 12V battery in series with the FC and imposing load current regulation. (a)

Fig. 11 . 4 . 2 . 3 . Test 6 :Fig. 12 .

 11423612 Fig.11. Test with 12V battery in series with the PEFC and imposing power regulation strategy.