Damien Besancenot
email: besancenot.damien@univ-paris13.fr.

Joao R Faria
email: rfaria2@utep.edu.

Kim Van Huynh

Kim Van

Huynh Congestion

Kim V Huynh
email: khuynh@u-paris2.fr

Congestion in academic journals under an impartial selection process

Keywords: Publication market, Academic journals, Editors, Congestion. JEL Classification: A11, C72, D82

Section 1: Introduction Following the trend set by the US many years ago, European and Asian governments are undertaking an institutional transformation of their research environment. The reforms aim at increasing the quantity and quality of research through performance-based reward schemes and enhancement of the role of research in the public evaluation process [START_REF] Geuna | University research evaluation and funding: An international comparison[END_REF].

In this process, academic publications tend to become the major indicator of research performance. As a result, competition for inclusion in the high impact peer-review academic journals becomes more intense and highly-cited journals attract more and more submissions4 . If this evolution reflects a desirable growth of knowledge production, it also presents adverse effects for the management of academic journals.

The editorial selection process is intrinsically imperfect. Journals may sometimes reject good papers and accept poor contributions to the scientific debate5 . Moreover, dealing with an increasing number of submissions, editors may face a shortage of resources required by the evaluation procedures. They may, for instance, be forced to ask reports from researchers whose expertise or motivation cannot be properly assessed [START_REF] Tsang | The as-is journal review process: Let authors own their ideas[END_REF]. In this case, that could be referred to as the congestion of the editorial process [START_REF] Goel | Proliferation of Academic Journals: Effects on Research Quantity and Quality[END_REF], the efficiency of the papers' selection may be dramatically challenged.

In answer to this editorial congestion, editors of top-tier journals start to implement defence strategies, some of them running against the transparency of the publication process (Bence andOppenheim 2004a, 2004b). In order to prevent submission of low quality papers, editors generally raise the costs paid by the authors in case of rejection. For example, a long time lag between the submission and the first decision, as it postpones the possibility of publication in other journals and the reward that could come with the publication, may deter low quality articles of being submitted (Elisson 2002[START_REF] Azar | The review process in economics: is it too fast?[END_REF]. The increase in submission fees appears to be an alternative efficient device to reduce the flow of submissions [START_REF] Wang | Competition, Wage commitments, and application fees[END_REF][START_REF] Leslie | Are Delays in Academic Publishing Necessary?[END_REF][START_REF] Azar | The academic review process: How can we make it more efficient ?[END_REF]). More recently, desk rejection policies tend to be implemented by an increasing number of journals (Besancenot et alii 2011) 6 . The editor may then decide to return a manuscript without review on the basis of various considerations, including expected probability of meeting the standards of the Journal, breadth of topic, interest to the journals audience. While these measures do oppose the congestion effect, they clearly convey an image of unfairness and lack of transparency.

This paper aims at considering the potentially detrimental effects of the increase in the number of submissions on the quality and the suitability of the papers' selection by the editors of academic journals. In this purpose, our paper develops a highly stylized model to study the publishing game played by researchers and editors 7 . It analyzes the conditions for congestion to appear in the editorial process and studies the effects of a rise of the rejection costs as a solution to avoid the congestion effect.

The main argument of this paper follows an idea close to [START_REF] Mccabe | Open Access and academic Journal Quality[END_REF] and Besancenot and Vranceanu (2008b) in which the editors can only imperfectly determine an article's quality. It considers researchers who may publish their paper either in a book or in a refereed journal. Publishing an article in an academic journal has greater value, however the selection process is risky and a rejection is costly for a researcher.

In our paper, the quality of the refereeing process relies on the number of submissions received by the Journal. The editor who receives a paper ignores the quality of the paper and, in order to make her decision, she sends the paper to a referee in charge of the paper's evaluation.

The editor has at her disposal a pool of reviewers that splits into two groups. A first group of referees have a faultless judgement. They can identify a paper's quality without error, rejecting poor papers and accepting good ones. These referees are perfectly known by the editor: they may be close colleagues from the same university or institution, regular authors of a journal or identified specialists of the field, in sum, they are members of the same academic network [START_REF] Van Dalen | The golden age of Nobel economists[END_REF][START_REF] Faria | Scientific, business and political networks in academia[END_REF]. However, the set of academic fellows in which an editor can have an absolute trust is bounded and, even in asking more than one report to each of these referees, the maximum number of trustable referee reports that an editor can ask for is limited. When the number of submissions exceeds this maximum number of good referee reports, the editor will have difficulties to obtain reviews from individuals with appropriate expertise (Hochberg et alii. 2009) 8 . In this case, the editor is forced to rely upon reviewers of the second group. However, these referees are less reliable: some of them will be prone to accept any kind of paper (they are 7 See [START_REF] Faria | The game academics play: editors versus authors[END_REF] for an alternative analysis of the game between editors and researchers. 8 [START_REF] Bedeian | The Manuscript Review Process: The Proper Roles of Authors, Referees, and Editors[END_REF] stresses that editors do not necessarily know who is a competent referee in a particular area. In his survey, 54.7% of the authors recognized that they had been asked to referee a manuscript they were not competent to critique and more than one third (36.6%) reported that they still accepted to review the paper. afraid of rejecting a good paper) while others will reject most of the submitted papers (to avoid the risk of accepting a bad paper). Thus, when no good referee is available, the editor may wish to correct some of the bad referees' decisions. She will accept some papers rejected by too demanding referees and reject some of the papers accepted by referees that seem too indulgent.

A main assumption of the paper is that editors are seeking for fairness. As a gap between the frequencies of accepted papers by the two groups of referees would reveal a bias in favour of either rejection or acceptation, an impartial editor should correct the bad referees' decision in order to match the frequency of their accepted papers with the frequency of acceptation by good referees. Hereafter, this correction will be referred to as the impartial selection process9 :

The basic result of the editorial game under the impartial selection assumption is twofold. The first point is that when the editor can call for a sufficient (but reasonably low) number of good referee reports, a separating equilibrium always exists whatever the values of other parameters.

In this equilibrium, good researchers and only good researchers submit their papers to the journal and each paper is accepted. As a result, the quality of the journal reaches its highest level. The second result is that when the reward of refereed publications exceeds a given threshold, the selection process may be subject to congestion and two hybrid equilibria are feasible. In these equilibria bad researchers submit their papers to the journal hopping to get published and, as the flow of papers exceeds the availability of good referees, the refereeing process becomes imperfect. This gives a chance to low-quality papers to get published by the journal.

As usual in case of multiple equilibria, expectations are self-fulfilling. The researchers' beliefs concerning the quality of the editorial process determines the effective quality of the journal.

Given the selected equilibrium, the model allows a discussion of the various policies implemented by editors to avoid the congestion effect.

The paper is organized as follows. Section 2 introduces the main assumptions and analyzes researchers' payoffs. Section 3 presents the typology of equilibria and comments on their basic features. Section 4 provides a discussion of the results and a last section summarizes our conclusions.

Section 2: The model We consider a population of researchers of dimension one. Each researcher is endowed with a paper and has to choose a publication strategy.

There are two types of papers, the g-type (for "good"), which are high quality papers, and the b-type (for bad), which are low-quality papers that do not satisfy the quality standards for publication in a refereed journal. In order to simplify the presentation, hereafter we will refer to gtype researcher (resp. b-type) for an academic fellow endowed with a good (resp. bad) paper.

The frequency of g-type papers (resp. b-type) in the total set of papers is denoted by α (resp.

α - 1 ), with . 1 0 < < α
With a population of researchers of dimension one, α is also the number of g-type papers in the economy.

A researcher perfectly knows the quality of his paper. He can either submit this paper to an academic journal (J-strategy) or publish it in a book (B-strategy). Whatever its type, a paper's quality is sufficient to guarantee a publication in a book. Thus the B-strategy leads to the certain reward A researcher playing the J-strategy sends his paper to the editor of an academic journal. If the paper is accepted for publication, the reward is with However, the paper may be rejected and the author has no alternative other than to publish the paper in a book. In this case, the reward will be where denotes the cost for the researcher of an unsuccessful submission (i.e. the sunk submission fee, the frustration of being rejected or the financial consequences of a delayed publication).

.

b W j W . b j W W > c W b - c
Good referees come from a pool of high-skilled researchers (a small subset of authors). Let us denote by θ the maximum number of reports that the editor can ask from these referees. In the following we will restrict our arguments to the non trivial case where . 2 / 1 <

≤ θ α

. There is at least as much good referee reports as good papers 10 and the editor cannot affect a good referee to more than half of the total number of papers.

The model can be cast as a sequential game featuring two rational players: the researcher, who chooses his publication strategy, and the journal's editor who decides to publish or not the submitted papers. The typical sequence of decisions is the following: Time nature chooses the type of paper that the researcher will have to manage.

, 0 = t Time the researcher decides which of the two publication strategies he will implement.

He can publish his paper in a book and receive (in this case, the game is over) or send it to the editor and wait for her decision.

Time

the editor who receives a paper sends it to a referee. With a probability , 2 = t P , the paper will be evaluated by a good reviewer, and with a probability ) 1 ( P the paper is evaluated by a bad one. 11 Hereafter, P will be endogenously defined according to the relative number of submissions and good referees. By assumption, the choice of the referee is random; the editor cannot assign good reviewers to good authors (Cf. [START_REF] Hamermesh | Facts and myths about refereeing[END_REF].

b -c W b -c W b -c W j W b π π 1-π 1-π W j W j
b -c W b -c W b -c W j W b π π 1-π 1-π W j W j
Nat will be accepted (its author will receive When the referee is a bad one, the editor may refuse to follow his decision ). j W 12 . According to the Impartial selection assumption, making her own evaluation of the paper, the editor adjusts the frequency of the accepted papers to match it with the g-type papers frequency. 13 In order to present the results in a simple way, we assume that, in this case, the paper is accepted with a probability π equal to the frequency of g-type in the set of submitted papers whatever its quality.

Figure 1 presents the decision tree of the game.

The Impartial selection assumption is clearly a radical idealization of the true selection process. Faced to a non reliable referee, an efficient editor will correct the decision according to her own assessment of the paper and the acceptation probability should be linked to the quality of the paper. However, our assumption presents some interesting properties that reflect the true selection process.

First, this assumption allows considering a downgrading precision of the editors as the number of bad submissions increases. If the selection of the highest quality papers is certainly possible when the editor has only a few papers to reassess, in case of congestion of the editorial process the time that an editor may spend on each paper drops and the precision of the editors judgment decreases. In this case, the acceptance of low quality papers on a timely topic as well as the rejection of good but technical papers in topics out of the expertise field of the editor can both be feasible. This imprecision introduces a random dimension in the editorial decision that is captured by our assumption. In the model, the probability of publication of a b-type paper increases with the fraction of b-type papers submitted to the journal. 14 Second, our assumption adequately formalizes part of the editor's rationality. Indeed, when the journal receives no bad paper, case π =1, a rational editor should be disposed to publish every submitted papers and the overall frequency of the accepted papers should be equal to one. In the opposite limiting case, with a frequency of good papers' submission close to 0, an editor should be prompt to correct the bad referees' advices in a very restrictive way and to accept a given paper with a probability close to 0. In both cases, editorial rationality is captured by our assumption.

Let us denote by (resp.

l )

λ the probability that a researcher endowed with a g-type paper (resp. a b-type) plays the J-strategy and by

) 1 ( l -(resp. ) 1 λ
the probability of the B-strategy.

12 According to [START_REF] Starbuck | Turning lemons into lemonade: Where is the value in peer reviews?[END_REF], if the editorial golden rule should be "No reviewer is ever wrong!", this rule does not assert that the editor should always follow reviewers' advice. 13 Remark that this frequency is known by the editor who observes the rate of rejection by good referees.

14 Introducing the possibility for an editor to perfectly identify a finite number of papers would not change the main results of the paper.

According to these probabilities, the number of journal submissions is given by , ) 1 ( λ α α -+ l and the probability P for a submitted paper to be evaluated by a good referee is:

) 1 ( } ) 1 ( , 1 { min λ α α θ - + = l P
According to the impartial selection assumption, the frequency π of papers accepted by the journal matches the frequency of g-type papers in the set of submitted papers, so:

) 2 ( , ) 1 ( λ α α α π - + = l l Thus, the expected payoffs for a ] | [ s U E g
g-type researcher playing strategy are:

s ( ) [ ] [ ] ) 3 ( , } ) 1 ( , 1 { min 1 ) 1 ( ) 1 ( ) 1 ( ) 1 ( ] | [ ] | [ c W W l l W c W W P PW J s U E W B s U E b j j b j j g b g + - ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - + - - + - - = - - + - + = = = = λ α α θ λ α α λ α π π and the expected payoffs for a ] | [ s U E b
b-type researcher are given by:

( ) ( ) [ ] ( ) [ ] ) 4 ( } ) 1 ( , 1 { min 1 ) 1 ( ) 1 ( ) 1 ( ] | [ ] | [ c W W l l l c W c W W P c W P J s U E W B s U E b j b b j b b b b + - ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - + - - + + - = - - + - + - = = = = λ α α θ λ α α α π π
Section 3: Equilibria:

We can study now the Perfect Bayesian Equilibria of the game. An equilibrium is defined here as a situation where the researchers, expecting their colleagues to play a given strategy, carry out optimal strategies coherent with their expectations.

Remark first that, in this game, the J-strategy is strictly dominant for a g-type researcher.

Indeed, the expected reward of a submission to the journal is higher for the writer of a good paper than for the author of a poor one, . If, for a g-type researcher, the reward of a publication in a book was superior or equal to the reward expected from a submission in an academic journal, i.e.

, this journal would receive no submission from a b-type researcher,

] | [ ] | [ J s U E J s U E g b = < = ] | [ ] | [ J s U E B s U E g g = ≥ = 0 = λ
. But, in this case, according to Eq. (1), P=1, and,the g-type researcher would be sure both to be reviewed by a good referee and to be accepted for publication in case of submission. The condition,

, ] | [ ] | [ J s U E B s U E g g = ≥ =
thus requires , which contradicts our assumption about these values. The reward of a publication in a book cannot be superior or equal to the reward expected from a submission in an academic journal b j W W ≤ With g-type researchers always playing the dominant J-strategy, we must have , and the set of equilibria of the game restricts itself to a separating, a pooling, and two hybrid equilibria.

As the pooling equilibrium appears to be the limiting case of one of the two hybrids, this equilibrium will be presented in the appendix.

= l

Separating equilibrium

In this first equilibrium, g-type researchers submit to the journal and b-type publish in books, thus researchers' beliefs are:

1 , 0 = = l λ
For a b-type researcher, these beliefs imply:

( ) [ ] ) 5 ( } , 1 { min 1 ] | [ c W W c W J s U E b j b b + - ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ - + - = = α θ As , 1 } , 1 min{ = α θ
the expected reward of a submission to the journal is

( ). ] | [ c W J s U E b b - = =
Obviously, the b-type researcher will prefer to publish his paper in books. For both types of researchers, optimal strategies are consistent with the equilibrium beliefs.

Remark that this equilibrium is always feasible under the sufficient condition:

1 } , 1 min{ = α θ , i.e. if
.

α θ ≥

This condition states that as long as the number of good reviewers exceeds the number of submitted papers, any low quality paper will be rejected. The papers selection process is perfectly efficient and there is no incentive for a bad researcher to submit a paper to the refereed journal. The journal receives and publishes only good papers.

Hybrid equilibria

The model also allows equilibria in which b-type researchers, indifferent between the two strategies, randomly adopts the B-or the J-strategy. In this case, researchers' beliefs are given by: ] 1 , 0 [ ∈ λ and the expected payoffs of the J-strategy are:

( ) ( )[ ] ) 6 ( 1 ] | [ ) 1 ( ) 1 ( c W W c W J s U E b j b b + - - + - = = - + - + λ α α θ λ α α α
For the b-type researcher the indifference between the two strategies,

, implies

] | [ ] | [ J s U E B s U E b b = = = : ( ) [ ] ) 7 ( ) 1 ( 1 ) 1 ( c W W c W W b j b b + - ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - + - - + + - = λ α α θ λ α α α Note that this condition can only be true if λ α α θ ) 1 ( - + <1, i.e. if 1 < P
. After some manipulations, Eq. ( 7) can be stated as:

( ) ( ) [ ] [ ] [ ] ( ) ⎩ ⎨ ⎧ - + = > + - = + - = ⇔ + - + + - - + - - + = λ α α α θ θα α λ α α λ α α ) 1 ( 0 with 0 ) 8 ( ) 1 ( ) 1 ( 0 2 2 x c W W y y xy cx c W W c W W c b j b j b j
This equation presents two solutions for x and implies two solutions for λ : (  )

[ ] [ ] ) 9 ( , ) 1 ( 2 / 4 2 ) 1 ( 2 / 4 2 2 4 2 2 2 1 2 2 , 1 ⎪ ⎩ ⎪ ⎨ ⎧ - - + - = - - - - = ⇒ - ± = α θ α λ α θ α λ θ
) 1 /( 2 0 α α θ λ - - = .
In the model,

1 < P implies: ( ) , 0 ) 1 /( > - - > α α θ λ a condition that is satisfied with any of the two values of λ if: ( ) (
)

) 12 ( 0 2 2 2 ) 1 ( ) 1 ( 2 4 2 ) 1 ( 2 2 2 1 > - - - - ⇔ - - > - - - - ⇔ - - > c c y c y 1 1 < λ or . 1 2 < λ Hybrid 1: ] 1 , 0 [ 1 ∈ λ By definition: , 0 4 2 1 2 1 < - - - ⇔ < y c y c y θ λ
two cases are possible.

•

Case 1: In this case, the inequality

. 0 2 ≤ -c y 1 1 < λ is always true. As, , 4 θ c y > this condition implies c y c 2 4 ≤ < θ , which is possible as 5 . 0 < θ . In this case, ] 1 , 0 [ 1 ∈ λ is feasible under the necessary condition: ( ) [ ] ( ) ) 13 ( 2 4 2 4 α α α α θ θ - ≤ - < - ⇔ ≤ < c W W c c y c b j

•

Case 2: Remark first that, in this case, the condition

( ) ( ) ( ) [ ] ) 15 ( 1 1 1 b j W W c - < - - - θ α θ α
It is easy to check that, with , 5 . 0 < θ condition ( 15) is satisfied when ( 14) is true.

Finally, mixing conditions for 1 1 < λ in Case 1 and Case 2, we get the necessary and sufficient condition [NSC] for

1 0 1 < < λ : [ ] (
)

) 16 ( 4 : α α θ - > - c W W NSC b j
In this range of parameters, differentiation of Eq. ( 8) and ( 9

) 17 ( 0 4 4 2 2 ) 1 ( 0 4 ) 1 ( ) 1 ( ) 1 ( 2 2 1 2 1 1 1 < ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - - - - - - = > - - + - + - =
1 0 2 < < λ : ( ) [ ] ( ) ( ) ) 19 ( 1 ) 1 1 ( 4 c W W c b j θ α θ α α α θ - - - < - < - Remark that 1 2 = λ when [ ] b j W W -
reaches the upper bound. The pooling equilibrium appears to be the limiting case of the hybrid 2 equilibrium.

Finally, the differentiation of Eq. ( 8) allows to check that, in this equilibrium, an increase of the cost c would induce a drop of the b-type submissions, 0 / 2 < dc dλ and that a rise of the reward would produce the opposite result

j W : 0 / 2 > j dW dλ : ( ) [ ] [ ] ) 20 ( 0 4 4 2 2 ) 1 ( 0 4 ) 1 ( ) 1 ( ) 1 ( 2 2 2 2 2 2 2 > ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - - + - - = < - - + - + - - =

< -

the only feasible equilibrium is the separating one. When the spread exceeds the previous threshold, three equilibria coexist.

In the range,

( ) [ ] ( ) ( ) , 1 ) 1 1 ( 4 c W W c b j θ α θ α α α θ - - - - < - <
the separating equilibrium is still feasible, however the hybrid equilibria where the b-type researcher plays the J-strategy with either probability 1 λ or 2 λ also exists. Moreover, when

( ) ( ) [ ] b j W W c - < - - - θ α θ α 1 ) 1 1 (
, the hybrid 2 degenerates into a pooling equilibrium, an equilibrium that coexists with the separating and the Hybrid 1 equilibria.

to submit their paper to the Journal, but this coordination is made easier by the increase of the publication reward.

In the model, the two hybrid equilibria do not exhibit the same properties: while Hybrid 2 is stable, Hybrid 1 is not. In order to check this result, consider an increase in the reward of a refereed publication. In both equilibria this change comes associated with an increase in the expected utility of a submission to the journal and, in response, the frequency rise of the mean time before first answer, or the decreasing content of the referee reports are the main usual solutions to foster self-selection and to reduce the propensity of researchers to submit their b-type papers [START_REF] Moyer | Academic Journals: Policies, Trends and Issues[END_REF][START_REF] Leslie | Are Delays in Academic Publishing Necessary?[END_REF][START_REF] Azar | The review process in economics: is it too fast?[END_REF][START_REF] Azar | The academic review process: How can we make it more efficient ?[END_REF]).

In our model, an increase of these costs presents two consequences: it reduces the range of the parameters that are consistent with the hybrid equilibrium (the value ( submissions. It thus appears as an efficient device to limit the adverse effects of congestion.

However, the manipulation of these costs may be a double-edged sword. Indeed rising the submission fees or delaying the first answer are both a device against congestion and a signal that this congestion could occur. It may thus contribute to the building of beliefs that will induce b-type researchers to submit their paper and foster congestion.

Another remedy is for the editor to pre-assess the quality of a paper, limiting external assessments to those papers that have a better chance of being of the top quality. Indeed, editors who decide first which papers will be send to referees may keep in the selection process a number of papers that exactly fits with the number of trustable reviewers. Papers assessment would then be made by efficient referees and the probability of a bad paper publication would reach its lowest level. Moreover, as self selection would prevent bad paper to be submitted the risk of seeing an editor rejecting from desk an interesting paper becomes negligible. Under desk rejection, the set of feasible equilibria would be restricted to the sole separating equilibrium.

Conclusion

This paper studies the various equilibria that could result from a publishing game under an impartial selection process. It states that the rising pressure on researchers to publish in refereed journals may lead to multiple equilibria with a possibility of congestion of the journals' editorial process.

As long as researchers stay confident about the efficiency of the editors screening process, self-selection prevents authors of low quality papers to submit their work to refereed journals. These journals then receive only high quality papers and are able to publish only influential papers. However, when the reward of a refereed publication increases, the incentive to submit papers to academic journals could lead authors of low quality papers to take their chance in the refereeing process. In this case, some congestion in the editorial mechanism may occur and the accuracy of the selection process will be challenged. As bad papers could be accepted in case of congestion while good ones could be rejected, this effect is obviously detrimental to the quality of academic journals and to the efficiency of the process of knowledge diffusion.

Facing an increase in the number of submissions, editors often try to restrict the refereeing burden by raising the cost of a rejection for the authors. The model shows that this policy efficiently reduces the incentive for authors of medium or low quality to submit to refereed journals. However, as the implementation of such a policy reveals the risk of a congestion of the editorial process, the signal it conveys could help researchers to coordinate on the equilibrium with congestion and this finally could present counterproductive effects. Desk rejection appears as a better way to guarantee the occurrence of the separating equilibrium.

Unfortunately, this could also lead editors to only accept submissions of known authors, the ones with good reputation, therefore creating a club in which unknown authors will have no chance to publish. These measures, again, might be detrimental to research and journals' quality.

A solution for the reduction of the congestion burden might come from the increase in the number of academic journals [START_REF] Goel | Proliferation of Academic Journals: Effects on Research Quantity and Quality[END_REF]. As the number of journals follows a long run increasing trend it appears somewhat logical that the pool of top journals follow the same evolution, reducing the monopoly power of top journals. Such an evolution could reduce the number of submissions received by each journal, increase the global pool of good referees (as identified by the editors) and finally increase the feasibility of the efficient separating equilibrium.

In order to keep the analysis tractable, this paper is built on some restrictive assumptions. For instance the model considers that good referees make perfect assessment of the quality of the submitted papers. Low quality papers will be rejected with certainty by efficient referees while good papers will always be accepted. This is obviously a strong assumption that doesn't fit with the empirical literature16 . Besides, our description of the editors' behaviour receiving a report from a non reliable referee is rather radical. Future work should consider an editor that would correct bad referees' decisions with probabilities that reflect the intrinsic quality of the paper.

Moreover, a more realistic model should link the reward of a publication in a refereed journal to the mean quality of the journals' papers. Despite its limitations, the model is interesting as it stresses that a journal impact could be challenged in case of a radical change in authors confidence in its selection process. The fact that an increase in the reward of publications in a top tier journal may challenge the status of this journal raises important questions about the increasing importance of publication incentives in the general management of science.

Appendix: Pooling equilibrium

In this equilibrium, each researcher will play the J-strategy. Researchers' beliefs are thus Some simple calculus allows checking that condition (A1) is verified under condition (A2), so this last equation is also the necessary condition for this equilibrium. For a low cost c or an important difference between the rewards and , the congestion effect is at its maximum.

  the separating equilibrium would not exist.

  Fig.1

  Note that these two roots exist if and only if

  After substitution of by its definition, this last equation leads to the necessary and sufficient y condition for

  Figure 2. presents the feasible values of 1 λ and 2 λ according to the value of [ ] b j W W -.

  However, an increase in λ generates two opposite consequences for the probability of publication by the journal. It raises the probability simultaneously drops the probability π of being accepted by the editor in case of bad refereeing. Depending on the relative importance of these two changes, the rise in λ comes with an increase or a drop in the journal probability of publishing b-type papers.In the hybrid equilibrium 2, the rise of 2 λ implies a decrease in the probability of publication for bad papers15 . In turn, this reduces the expected reward of submission to the journal for a btype researcher and progressively offsets the initial increase of this reward. The model converges toward a new equilibrium with a higher 2 λ .The opposite effect is at work in the hybrid 1 equilibrium in which a higher propensity 1 λ for a researcher to submit its b-type paper increases the probability of publication for these papers. This reinforces the incentive for b-type researchers to submit their paper and contributes to a cumulative increase in λ . This effect is self sustaining until λ reaches the threshold 0 λ λ = , value for which any further increase in λ would induce a drop in the probability of b-type papers publication. The model then converges toward a type 2 hybrid equilibrium.In this model, the equilibrium values 1 λ define the frontier of the λ values leading to the hybrid 2 or the separating equilibrium. For any values of the parameters, an initial situation with would degenerate to an hybrid 2 equilibrium (resp. a separating equilibrium). As 1 λ is a decreasing function of the expected reward of a refereed publication, the higher this reward the easier for b-type researchers to coordinate on the hybrid equilibrium and to provoke the congestion of the editorial system.

  to the increase of the number of submissions, a possible editor reaction is to increase the cost c paid by the researchers in case of rejection. The increase of the fees, the 15 The derivative of ) 1 ( P -π with respect to λ is negative under condition 0 λ λ > , which is true for any λ in the hybrid 2 equilibrium and positive under condition 0 λ λ < , which is true for any λ in the hybrid 1 equilibrium.

  congestion, it contributes to the of the frequency of b-type papers'

.

  For a g-type researcher, the expected payoff of a submission is given by For a b-type researcher, the expected payoff of a submission is:

For instance, the Editor Report 2010 of the American Economic Review states that the number of submissions to the journal has increased from 641 in 1980 to 1398 in 2009 for a stable number of published papers (The American Economic Review, Report of the Editor, January 2, 2010).

This assumption is empirically verified by[START_REF] Oswald | An Examination of the Reliability of Prestigious Scholarly Journals: Evidence and Implications for Decision-Makers[END_REF] or[START_REF] Cherkashin | The inside scoop: Acceptance and rejection at the journal of international economics[END_REF] who show that the best article in a medium quality journal can be more influential than the worst articles in an issue of a top tier journal. See also[START_REF] Gans | How Are the Mighty Fallen: Rejected Classic Articles by Leading Economists[END_REF] for a description of the difficulties encountered by famous seminal papers to be published.

See for instance the Instruction to Authors web page of Econometrica, Journal of Monetary Economics Scandinavian Journal of Economics or The American Economic Review.

The assumption of impartiality in decision making has been introduced byBesancenot and Vranceanu (2008a) in the description of a judge behaviour seeking for impartial justice under congestion of the court.

[START_REF] Starbuck | Turning lemons into lemonade: Where is the value in peer reviews?[END_REF] underscores that one of the most striking feature of referee reports is their inconsistence (counting "accept"=1, "reject"=-1 and "revise" as 0, the correlation of the reviewers decision is equal to 0.12).

In case of multiple equilibria, the prevailing equilibrium relies on the players' beliefs. As long as researchers expect a perfect refereeing process, they do not submit b-type papers. In this case, submission is restricted to the sole g-type papers. The editor receives a low number of submissions and may only call for efficient reviewers. Expectations are self-fulfilling. On the opposite, when a researcher believes that the papers' selection is imperfect, he may submit a low quality paper hoping that the overwhelmed editor will send it to an inaccurate referee.

Massive submissions from b-type researchers thus lead to the congestion of the editorial process and induce the deterioration of the selection process.

Since academic publications tend to become the most prevalent measure of research performance, the value of a publication in a scientific journal is steadily increasing and, as a result, the number of submissions is growing at a dramatic speed. According to our model, as long as the submitted papers are of the g-type, this does not affect the quality of academic journals. However, when the reward of peer reviewed publications exceeds the threshold some authors may also submit their When this occurs, the quality of the selection process is being severely challenged and the mean quality of the published papers drops.

Note that the switch from an equilibrium to another is not continuous: as λ jumps from zero to a strictly positive value, the quality of the published papers drops sharply. Of course, such a change implies the implicit coordination of the b-type researchers who must collectively decide


Matias Duran-Matute

Gabriella Di Nitto

Ruben Trieling

Gertjan Van Heijst

Instabilities and transition in three-dimensional flows with rotation TRANSITION FROM QUASI-2D TO 3D IN A ROTATING ELECTROMAGNETICALLY FORCED DIPOLAR FLOW STRUCTURE

Introduction

Background rotation is assumed to enforce the two-dimensionality of flows. If the rotation is fast enough, the flow far away from the boundaries becomes independent of one coordinate. Furthermore, the characteristics of the boundary layers that form next to the boundaries perpendicular to the rotation axis (known as Ekman boundary layers) allow to model the evolution of decaying rotating flows using the two-dimensional vorticity equation

Dω Dt = λ Ek ω, (1)
where D/Dt is the material derivative, ω is the vorticity component parallel to the rotation axis of the system, and λ Ek is a constant known as the Ekman damping coefficient. If a flow obeys eq. ( 1), the flow can be said to be quasi-two-dimensional [START_REF] Dolzhanskii | An advanced experimental investigation of quasi-twodimensional shear flows[END_REF]. Equation ( 1) is a priori only valid if the Coriolis acceleration is much stronger than the advective acceleration (i.e. the Rossby number Ro is small) and if the flow evolves freely.

In the current work, we determine experimentally the limit of applicability of the linear Ekman theory, on which eq. ( 1) is based, to flows driven by a non-conservative body force. In other words, we determine the transition in the parameter space between a quasi-two-dimensional and a three-dimensional flow. In particular, we study a dipolar flow structure driven by time-independent electromagnetic forcing in a shallow fluid layer subjected to background rotation, and we characterize the response of the flow as a function of the parameters of the problem. The limit for the two-dimensionality of the flow is reflected as a change in the scaling of the response of the flow to the magnitude of the electromagnetic forcing, and against the common belief, it does not depend exclusively on the Rossby number.

Methods

The experiments were carried out in a water tank with a base of 34 × 30 cm 2 placed on top of a rotating table, which rotates at a frequency Ω. The tank is filled with a salt solution with a concentration of 178 g l -1 with a kinematic viscosity ν = 1.50 • 10 -6 m 2 s -1 and a density ρ = 1190 kg m -3 to a depth H and covered with a transparent perspex lid to avoid free-surface deformations. To force the flow, two titanium electrodes are placed along two opposite sides of the tank, and three 30 × 10 cm 2 rectangular magnets are placed 1.1 cm underneath the tank bottom. The magnitude of the magnetic field of each these magnets is 0.018 T measured just above their centre. The magnet at the centre has its North Pole facing up, while the two side magnets have their North Pole facing down. A constant electric current I is applied through the fluid using a power supply with a precision of 10 -2 A.

Particle Image Velocimetry (PIV) is used to measure the horizontal velocity field of the flow in a plane at mid-depth. The fluid is seeded with 106-150 µm polymethylmethacrylate (PMMA) particles, which are illuminated at mid-depth with a laser sheet produced by a double pulsed Nd:YAG laser.

Numerical simulations of the flow were performed using a finite-element code (COMSOL). These simulations serve two purposes: (1) to obtain the three-dimensional velocity field of the flow and (2) to reach regions of the parameter space that are inaccessible experimentally.

Non-dimensional parameters

Dimensional analysis yields three independent dimensionless control parameters:

Ch ≡ IBH ρν 2 , Ek ≡ ν ΩH 2 , δ ≡ H L , (2)
where the Chandrasekhar number Ch characterizes the EM forcing and represents the ratio of the Lorentz force to the viscous force; the Ekman number Ek characterizes the system's rotation rate and represents the ratio

of viscous forces to the Coriolis force; and the aspect ratio of the container δ characterizes the geometry of the flow domain. B is the magnitude of the magnetic field at mid-depth above the center of a magnet. In addition, as the response parameter of the problem, we define the Reynolds number

which represents the ratio of inertia forces to viscous forces, with U the spatial average of the horizontal velocity at mid-depth. In other words, Re = Re(Ch, Ek, δ). The Rossby number can be written in terms of the other dimensionless parameters as Ro = δ 2 EkRe/2.

Results

Figure 1 presents the response of the flow as function of the forcing for experiments and simulations with Ek = 3.5 • 10 -3 and different values of δ. Note that the axes have been multiplied by δ 2 , resulting in the collapse of the curves for different δ-values. As can be seen, there are two scaling regimes for all Ek-values. For small values of Chδ 2 there is a linear regime where Re ∝ Ch, while for large values of Chδ 2 , there is a non-linear regime where Re ∝ Ch 1/2 . The transition reflects the growing importance of the advective acceleration, and is similar to the transition found in the case of shallow flows without background rotation [START_REF] Duran-Matute | Scaling and asymmetry in an electromagnetically forced dipolar flow structure[END_REF].

From dimensional analysis, it can be estimated that the transition between the two different regimes occurs when

showing that it does not depend exclusively on the Rossby number.

For strong background rotation (small Ek-values), viscous dissipation is dominated by Ekman damping in the linear regime. However, numerical simulations show that the Ekman boundary layers are deformed in the non-linear regime. Hence, linear Ekman damping is no longer a good approximation in this regime, and the flow cannot be considered as quasi-two-dimensional. This can be true even for small Ro-values. The deformation of the Ekman boundary layers is then not due to non-linearities in the bulk of the fluid. Instead, the balance between viscous forces and the Coriolis force, which essential for the existence of Ekman boundary layers, is broken due the electromagnetic forcing within the boundary layer.


Clément Jause-Labert
email: clement.jause-labert@ec-lyon.fr

Fabien S Godeferd

Instabilities and transition in three-dimensional flows with rotation CONFINEMENT OF TURBULENT FLOWS WITH ROTATION EFFECTS WITH A PENALIZATION METHOD

Laboratoire de Mécanique des Fluides et d'Acoustique

École Centrale de Lyon, Université de Lyon, France.

We want to analyse the structuration and dynamics of homogeneous turbulence in a cylindrical container with open periodic ends, placed in a rotating frame. To that extent, we performed pseudo-spectral Direct Numerical Simulations at different Rossby and Reynolds numbers using a penalization technique to take into account the radial confinement.

A first part of the presentation is dedicated to the validation of this numerical method by considering the impact of a vortex ring on a flat "penalized" wall and compare the results obtained with the existing experimental data. A second part will then describe the dynamics of the cylindrical flow as well as its anisotropic structure and its main Lagrangian statistics.

Context and motivation

Homogeneous turbulence is obviously an idealized picture of actual or experimental flows, as boundaries are always present in nature. Moreover, actual flows in nature or in industry are also subjected, to a certain extent, to body forces such as the Coriolis force when considering rotation effects in geophysical flows, buoyancy in the case of stratified flows or the Lorentz force in the case of an electrically conducting fluid submitted to a magnetic field.

In the present work, we propose to explain some basic features of turbulent flows in a cylindrical enclosure, a geometry which bears some similarities with current experimental settings for studying high Reynolds number turbulence (von Karman flows). This geometry is also chosen because it retains homogeneity in two directions (the azimuthal and the vertical ones). We also propose to add to this confined flow the effect of the Coriolis force that appears when considering background rotation. We will take advantage of the axis of symmetry of the confinement and align the axis of rotation with it. This configuration will allow to evaluate the effect of confinement onto rotating turbulence, and contrast its properties with the well-described dynamics of homogeneous rotating flows [START_REF] Cambon | Energy transfer in rotating turbulence[END_REF].

Presented work

We use a tri-periodic pseudo-spectral code with an immersed boundary method, namely the volume penalization method. This class of methods has been introduced in 1972 by Peskin (see [START_REF] Peskin | Flow patterns around heart valves: A numerical method[END_REF]) and allows the computation of bounded flows on Cartesian grids (meaning that no refinement close to the boundary is needed). The method consists in adding an external force field in the Navier-Stokes equations, where a mask function splits the computational mesh between fluid and solid/porous regions. A penalization parameter allows to describe an impermeable domain in the asymptotic zero limit. A mathematical demonstration of the convergence of the penalized equations to the Navier-Stokes ones with no-slip boundary conditions has been achieved by Angot et al. [START_REF] Angot | A penalization method to take into account obstacles in incompressible viscous flows[END_REF]. However, when computing the set of penalized equations with an explicit scheme for evaluating the penalized term, a stability issue appears which hardly constrains the time-step. An original way to avoid this restriction has been developed and is formulated in [START_REF] Jause-Labert | Numerical validation of the volume penalization method in three-dimensionnal pseudo-spectral simulations[END_REF]. In the latter work, we also highlight the fact that the penalization term is compressible and explicitly acts on the pressure term.

First, we propose to test the numerical method by considering the impact of a vortex ring on a wall introduced thanks to the penalization method. Walker et al. [START_REF] Walker | The impact of a vortex ring on a wall[END_REF] showed that, in a defined range of Reynolds number, a secondary ring is created and the interaction of those two vortex rings leads to a third one. The comparison of our simulations with this experimental work (see figure 1) is very interesting and reveals that the penalization method is able to reproduce the features described in [START_REF] Walker | The impact of a vortex ring on a wall[END_REF].

We then perform Direct Numerical Simulations (DNS) of confined freely decaying turbulence with and without the addition of the Coriolis force to observe and compare the decay of such flows. A qualitative viewpoint is given by figure 2 at the beginning of the computation. Some trajectories of tracer particles are used to obtain a Lagrangian viewpoint of the global effect of confinement. The principal goal of this work is to present the variation of different statistics in the flow depending on the distance to the wall. Such statistics are the orientation of the velocity vectors, the pdf of the different components of the velocity, the radial evolution of the normalized rms velocities, the directional length scales, etc. Figure 2 shows the radial distribution of the three rms velocities in the cylindrical coordinates.

Our presentation during Euromech Colloquium 525 will include Eulerian statistics from an extended database with high resolution DNS, as well as Lagrangian dispersion statistics.

EUROMECH

  Colloquium 525, 21-23 June 2011, Écully, France Instabilities and transition in three-dimensional flows with rotation

Figure 1 :Figure 2 :

 12 Figure 1: Impact of a vortex ring on a flat wall -Re=1250. Creation of secondary and tertiary vortex rings. Left : Experimental observation by Walker et al.. Right : Present penalized simulation with η = 10 -6 , visualization of the enstrophy field.


A Pieri

C Cambon

F S Godeferd

Instabilities and transition in three-dimensional flows with rotation A STUDY OF HOMOGENEOUS TURBULENCE WITHIN BAROCLINIC CONTEXT

e present direct numerical simulations and linear models for homogeneous turbulence submitted to the combined distorsions of constant vertical mean shear, vertical solid body rotation and vertical stable stratification, representative of situations in geophysical flows. Depending on the parameters, optimally reduced to the Richardson number and a baroclinic parameter, the baroclinic instability is triggered and modifies the dynamics and structure of the flow. We characterize turbulence in these different states, which present specific anisotropic features, using physical-space quantities (energies, correlation lengths, velocity structure functions) and spectral statistics (directional poloidal/toroidal/potential energy spectra).

Introduction to the baroclinic context in turbulent flows

The baroclinic context is characterized by a superposition of three coupled phenomena, required for the existence of baroclinic instability: (1) the Coriolis force, caused by earth rotation in geophysical flows; (2) stable stratification due to density gradients in the atmosphere, which lead to buoyancy forces in the vertical direction;

(3) high vertical velocity gradients, as at the altitude of the tropopause in atmospheric flows, in the form of jet streams, which, in first approximation, are modelled by homogeneous shear. Due to admissibility conditions [1,8], a spanwise density gradient is necessarily created and added to the previous vertical one. Under these conditions, tilting of isopycnal surfaces is induced [START_REF] Pedlowsky | Geophysical Fluid Dynamics[END_REF], and, although the mean density gradients are stable in the sense that they lead to positive restoring forces, the misalignment of isopycnal surfaces with the horizontal plane can lead to unstable dynamics [START_REF] Pedlowsky | Geophysical Fluid Dynamics[END_REF][START_REF] Drazin | Hydrodynamic stability[END_REF], hence the baroclinic instability.

The first works on baroclinic instability where done by [START_REF] Charney | [END_REF] [START_REF] Charney | [END_REF] using quasi-geostrophic equations in the β-plane approximation. He derived a necessary condition for instability to occur formulated simply by an inequality implying the Rossby radius of deformation. Further contribution by Eady (1949) [17] using the f -plane approximation was later added. Eady considered a simpler model -a Couette-like configurationof the atmosphere and obtained an instability condition resting on a critical wavenumber [START_REF] Pedlowsky | Geophysical Fluid Dynamics[END_REF]. Following Eady, we also place the study within the f -plane approximation. We replace the two-boundary plates approximation by an infinite Couette flow to model shear effects [START_REF] Rogallo | Nasa Technical Memorandum[END_REF].

DNS results of baroclinic turbulence

Investigations of homogeneous turbulent flows submitted to the separate effects of homogeneous shear, stable vertical stratification or rotation were done in the past decade [2,3,4,5,6]. Here, we focus on the following new approach: Direct Numerical Simulation (DNS) of homogeneous turbulence including the complete coupled three previous distorsions -the so-called 'baroclinic' context. Unlike the previously mentioned contexts, the baroclinic instability is a reservoir of energy which does not impose to add an artificial forcing to the simulations, or to have to deal with decaying flows. The aim of our study is first to provide a detailed characterization of the Eulerian properties of developped baroclinic turbulence. The parametric space is very large, since it not only includes the properties of turbulence itself, Reynolds number, cut-off wavenumbers, but also the choice of the intensities of rotation, stratification and shear. A reduction of the parametric space is obtained by considering the Richardson number defined as Ri = N 2 /S 2 and the baroclinic parameter ε = Sf /N 2 which is also the mean slant angle of the isodensity surfaces. Here, S = ∂ y U x is the mean velocity gradient, N = (-g∂ y ρ/ρ 0 )

1/2 is the Brunt-Väisälä frequency and f = 2Ω is the rotation rate. We shall investigate ranges of these parameters between [0 : 2] for Ri and [0 : 1] for ε. The Navier-stokes equations in the Boussinesq approximation are solved using pseudo-spectral Direct Numerical Simulation. Periodicity is assumed in the three directions. Under the action of shear, the mesh is deformed and a periodic remeshing is needed using the algorithm by Rogallo [START_REF] Rogallo | Nasa Technical Memorandum[END_REF] (the anisotropic adaptation of the Orszag-Patterson algorithm) in spectral space (p, q, r). De-alisasing is done following Delorme [12] method. The code used in this study is a MPI-based parallel code : the turbulence box is cut into slabs following the algorithm by Coleman et al. [START_REF] Coleman | [END_REF]. Fast Fourier transforms are done using the library FFTW by Frigo and Johnson [START_REF] Frigo | FFTW for version 3.1[END_REF]. Time-advancing is done according to the third order Runge-Kutta (RK3) method. Lastly, the rotational form of the non-linear term has been implemented. We start by considering twopoint spectra of Eulerian velocity and buoyancy fields, as well as the evolution of additional scalars which are introduced in the flow, with different Schmidt numbers. The time evolution of quantities such as the deviatoric part of the Reynolds stress tensor, the componentality and dimensionality tensors [7,9], potential and kinetic energy directional spectra are analized to bring out and understand the complex anisotropic structure of the flow. A link with extended structure functions is also proposed, in order to assess the possible application, or disagreement, of scalings available for isotropic turbulence in the context of Kolmogorov theory. We will also study two-point correlations for characterizing the turbulent structures, and their properties. Large scale structures will be quantified with directional correlation length obtained from the velocity correlation tensor, whereas two-point vorticity correlations put to the fore smaller turbulent structures. The Lagrangian properties are also studied, and related to Eulerian data, especially considering the dual characterization of anisotropy. To refine our study, we thus obtain results concerning mixing properties of the flow by looking at both the stratifying agent concentration (see for instance the distribution of buoyancy on figure 1) and passive scalars advection. We also put the emphasis on the analysis of possibly unstable dynamics of turbulence within the baroclinic context, in a second part. Inertial transfers will be investigated, considering energy exchanges between the kinematic and the potential modes, but also the interscale and directional energy drain. This structuring of the flow, of nonlinear, irreversible nature since it is due to quadratic terms in the equations, is also compared to the predictions of linear theory (often called Rapid Distorsion Theory, RDT), which provides lots of valuable information on the spectral energy distribution reorganization by the mere body forces (Coriolis and buoyancy) and shear. Since RDT is also computationally much lighter than DNS, it also permits a preliminary opening of the parametric space, allowing to choose the most relevant parameters for the high resolution simulations.

EUROMECHFigure 1 :

 1 Figure 1: Sketch of the mean flow (left). Buoyancy distribution (right). DNS with 512x768x512 degrees of freedom with Richardson number Ri = 0.5 and baroclinicity parameter ε = 0.2. Re λ (0) = 44.1 and Sk ǫν = 2.55. With ǫ ν the kinetic energy dissipation. τ = tS = 7.