Our main conclusion is that fluctuations are large: for both the energy loss at large angles and the gluon multiplicity N (x 0 ), the dispersion is parametrically as large as the respective average quantity. Such large fluctuations should be easy to observe inevent-by-event studies of the di-jet asymmetry at the LHC. In particular, we predict that the multiplicity fluctuations should exhibit Koba-Nielsen- Olesen (KNO) scaling [ 43 ]. A similar scaling is known to hold for a jet branching inthe vacuum [ 44 ], but themedium-induced gluon distribution is found to be considerably wider (see Sect. 4 for details). The physical picture emerging from our analysis can be summarized as follows. In a typical event, the leading particle evolves by emitting a number of order one of primary gluons with energy ω ∼ ω br (L) together with a large number ∼ [ω br (L)/ω] 1/2 of considerably softer gluons, with ω ω br (L). Here, ω br (L) ≡ ¯ α s qL ˆ 2 , with ¯ α s = α s N c /π and L the distance travelled bythejet through themedium, is the characteristic energy scale for medium-induced multiple branching. (We implicitly assume here that ω br (L) E, as this is the typical situation for high energy jets at the LHC; see the discussion at the end of Sect. 2.1 .) The primary gluons with ω . ω br (L) develop mini-jets via successive democratic branchings and thus transmit their whole energy to softer quanta with ω ∼ T that are expected to thermalize via collisions inthemedium [ 42 ]. Harder emissions with ω ω br (L) occur only rarely, with a small probability ∼ [ω br (L)/ω] 1/2 , and moreover they do not contribute to the energy lost bythejet as a whole, since hard gluons propagate at small angles. The energy loss at large angles is rather controlled bythe hardest typical emissions, those with energies ω ∼ ω br (L). As aforementioned, the number of such emissions is of order one and they occur independently from each other; accordingly, both the average energy loss bythejet and its dispersion are of order ω br (L) (see Eq. ( 3.15 )).
We study the gluon distribution produced via successive medium-induced branchings by an energetic jet propagating through a weakly-coupled quark-gluon plasma. We show that under suitable approximations, thejetevolution is a Markovian stochastic process, which is exactly solvable. For this process, we construct exact analytic solutions for all the n-point correlation functions describing the gluon distribution inthe space of energy [1, 2]. Using these results, we study theevent-by-event distribution of the energy lost bythejet at large angles and of the multiplicities of the soft particles which carry this energy. We ﬁnd that theevent-by-event ﬂuctuations are huge: the standard deviation inthe energy loss is parametrically as large as its mean value . This has important consequences for the phenomenology of di-jet asymmetry in Pb +Pb collisions at the LHC: it implies that the ﬂuctuations inthe branching process can contribute to the measured asymmetry on an equal footing with the geometry of the di-jetevent (i.e. as the di ﬀerence between thein-medium path lengths of the two jets). We compute the higher moments of the multiplicity distribution and identify a remarkable regularity known as Koba-Nielsen-Olesen (KNO) scaling . These predictions could be tested via event- by-event measurements of the di-jet asymmetry.
[z(1 − z)] 3/2 = K(1 − z) , f (z) ≡ 1 − z(1 − z) 5/2
It depends only upon the splitting fraction z since the corresponding dependence upon the energy (fraction) x of the leading particle, cf. Eq. ( 3.2 ), has been explicitly factored out in writing Eq. ( 3.4 ). We shall refer to the r.h.s. of Eq. ( 3.4 ) as the ‘branching term’ and denote it as ¯ α I[D]. This is the sum of two terms, which can be recognized as the familiar ‘gain’ and ‘loss’ terms characteristic of a branching process. The first term, which is positive and nonlocal in x, is the gain term : it describes the rise inthe number of gluons at x due to emissions from gluons at larger x 0 = x/z. The respective integral over z is restricted to x < z < 1 bythe support of D(x/z, τ ). The second, negative, term, which is local in x, represents the loss term and describes the reduction inthe number of gluons at x due to their decay into gluons with smaller x 0 = zx. Taken separately, the gain term and the loss term in Eq. ( 3.4 ) have endpoint singularities at z = 1, but these singularities exactly cancel between the two terms and the overall equation is well defined.
Besides the emblematic studies of the Higgs boson and the search of new physics beyond the Standard Model, another goal of the LHC experimental program is the study of the quark- gluon plasma (QGP), a phase of nuclear matter that exists at high temperature or density, and in which the quarks and gluons are deconfined. This state of matter is now re-created inthe laboratory in high-energy nucleus-nucleus collisions. To probe the properties of the QGP, a very useful class of observables refers to the propagation of energetic jets. A jet is a collimated spray of hadrons generated via successive parton branchings, starting with a highly energetic and highly virtual parton (quark or gluon) produced bythe collision. When such a jet is produced inthe dense environment of a nucleus-nucleus collision, its interactions with the surrounding medium lead to a modification of its physical properties, phenomenon known as jet quenching. In this thesis, we develop a new theory to describe jet quenching phenomena. Using a leading, double logarithmic approximation in perturbative QCD, we compute for the first time the effects of themedium on multiple vacuum-like emissions, that is emissions triggered bythe virtuality of the initial parton. We show that, due to the scatterings off the plasma, thein- medium parton showers differ from the vacuum ones in two crucial aspects: their phase-space is reduced and the first emission outside themedium can violate angular ordering. A new physical picture emerges from these observations, with notably a factorisation in time between vacuum- like emissions and medium-induced parton branchings, the former constrained bythe presence of themedium. This picture is Markovian, hence well suited for a Monte Carlo implementation. We develop then a Monte Carlo parton shower called JetMed which combines consistently both the vacuum-like shower and themedium-induced emissions.
annually ( Fig. 2 ). Wine-growing developed here on a fault-
scarp relief inthe Middle Ages ( Dion, 1959 ). These historical
hillslopes, inducedbythe Bressan rifting, form the eastern border of the Burgundy plateau. The hillslopes develop on Middle to Upper Jurassic limestones and marls, and are covered by colluvium soils of argillaceous-gravelly nature and formed by Weichselian cryoclastic deposits (“grèzes litées”) reaching up to 3 m thick ( Journaux, 1976 ). Soils were described fol- lowing the method of Baize and Girard (1995) . These deposits are draining, non-cohesive, easily erodible and display a low organic content (b1%) like all vineyard soils in Côte-d'Or ( Mériaux et al., 1981 ). Measured dry soil bulk density of the soil top layer varies between 1.25 and 1.5 t m-3. The texture is rather homogenous over the whole plot and is composed of 40% of clays and silts, 50% of gravels (2 mm to 10 mm) and a low sand and boulder content. The topsoil are ploughed ( Mériaux et al., 1981 ). The argillaceous aggregates with polyhedral blunted to grained form are slightly structured. No pedogenetic segrega- tion has been observed.
Key words. Galaxies: evolution – Galaxies: kinematics and dynamics – Galaxies: interactions – Methods: N-body simulations
The formation of disk galaxies remains an outstanding puzzle in contemporary astrophysics (see Mayer et al. 2008 for a re- view). According to hierarchical models of structure formation, mergers and interaction of galaxies are an essential ingredient of galaxy formation and evolution. Earlier works and numerical simulations show that the remnants of mergings of purely stel- lar progenitors are more likely to be elliptical galaxies (Toomre 1977; Barnes 1988; Barnes & Hernquist 1992; Hernquist 1992; Lima-Neto & Combes 1995; Balcells & Gonz´alez 1998; Naab et al. 1999 etc.) and recent studies extended this result to gas- rich progenitors (Springel & Hernquist 2005; Robertson et al. 2006; Hopkins et al. 2008). Whether this is compatible, or in- compatible, with the fraction of disk galaxies present inthe lo- cal universe depends on the typical number of expected merg- ers by galaxy (see for instance Kazantzidis et al. 2007). Such predictions seems to be incompatible with observations which suggest that disk galaxies represent the majority (70%) of the galaxy population observed inthe local universe (see Hammer et al. 2005; Nakamura et al. 2004 and references therein). To help resolve such issues, Hammer et al. (2005) suggested that disks can be rebuilt during the encounters of gas rich spirals. Indeed such proposition was guided bythe remarkable coinci- dence of the redshift increase, up to z=1, of the merger rate,
Jet quenching has been observed at RHIC [12, 13, 14, 15] and at the LHC  via the measurement of high p t hadron inclusive production and correlations, which are observed to be strongly suppressed in
central A–A collisions compared to a scaled pp reference. These high p t hadron observables have been
the major tool for measuring the energy loss of hard scattered partons and thereby the properties of themedium, but they provide only indirect and biased information on the parton evolutioninthemedium. The aim of full jet reconstruction is to measure jet modifications due to energy loss in an unbiased way [17, 18]. Already first measurements of reconstructed jets in heavy-ion collisions at the LHC showed an energy imbalance between back-to-back dijets, which is attributed to jet quenching [9, 19].
(Q + l) 2 − l 2 K Q, l, z, xp + 0 ,
(4.8) where the lower limit x inthe integral over z, which was a priori present only inthe ‘gain’ term, has also been inserted inthe ‘loss’ term, while at the same time multiplying the latter by a factor of 2, to account for its original singularities at both z = 0 and z = 1 (which is legitimate since, to the accuracy of interest, the integral is controlled by values z ' 1 x). The particular combination of momenta, (Q + l) 2 − l 2 , that emerges then in Eq. ( 4.8 ) can be given the following interpretation: when z ' 1, Q ≡ k − z(q + l) is the same as (minus) the transverse momentum q + l − k of the unmeasured daughter gluon. Hence Q + l ' k − q is the change in transverse momentum at the emission vertex, with two obvious components: the momentum l acquired via medium rescattering during the branching process and the momentum Q taken away bythe unmeasured daughter gluon. The above applies to the ‘gain’ term. For the ‘loss’ term, there is no real emission, so the only source of momentum broadening is the momentum l transferred from themedium. The difference (Q + l) 2 − l 2 represents therefore the net change inthe transverse momentum squared, and the average of this quantity over the (momentum dependent) splitting kernel yields the correction δ ˆ q.
this odd mode is the small difference between the partic- ipant numbers of projectile and target nuclei inducedbyfluctuations, which creates a forward-backward asymme- try of the multiplicity [29, 30]. Since both the colliding system and the analysis window are symmetric around η = 0, principal components have definite parity in η, up to statistical fluctuations. Indeed, the next mode v 0 (3) (η) is even, suggesting that principal components typically have alternating parities. The corresponding eigenvalue is again much smaller, λ (3) ∼ λ (2) /5. v (4)
Heavy-ion collisions, fluctuations, anisotropic flow
It was recently realized that the understanding of fluctuations, in particular fluctuationsinthe initial state, is an essential ingredient inthe analyses of ultra-relativistic heavy-ion collisions . To characterize a fluctuating initial state theoretically, e ffective models have been proposed by properly introducing fluctuations on top of nucleus-nucleus collisions [2, 3]. However, despite some success of these models, the initial state of heavy-ion collisions still con- tributes a major fraction of the uncertainty of quantitative predictions [4, 5]. In experiments, initial state fluctuations can be revealed bythe study of anisotropic flow v n . Defined as the Fourier harmonics of the corresponding particle spectrum, v n reflects the property of bulk medium expansion, and its response to the initial state anisotropy. Taking into account thus the direct mapping between v n and initial anisotropy, which is commonly formulated as eccentricity ε n , it is expected that event-by-event (EbyE) distribution of v n is largely determined byfluctuations of ε n . Indeed, many non-trivial observations have been made in heavy-ion experiments regarding flow fluctuations, among which the EbyE distribution of v n in Pb-Pb collisions , and cumulants of elliptic flow v 2 from p-Pb collisions [7, 8] will be discussed in this work. In this paper, without detailed modeling of initial state we propose a new parameterization to describe ε n fluctuations. As will be shown in Section 2, the crucial improvement of our new parameterization is rooted inthe fact that |ε n | ≤ 1. The universality of parameterizing fluctuations of ε n will be addressed also in Section 2. In Section 3 we apply the parameterization to the measured flow cumulants and flow distribution.
What is theevent B method? Inthe sequel, we refer to the original B method as classic B [ABR 96] and its event-based evolution as event B. Theevent B method [ABR 03a, ABR 98] reuses the set-theoretical and logical notations of the B method [ABR 96] and provides new notations for expressing abstract systems or simply models based on events. Moreover, the refinement over models is a key feature for incrementally de- veloping models from a textually-defined system, while preserving correctness; it im- plements the proof-based development paradigm. Each development. includes proofs for invariance and refinement. Operations of the B classical method do not exist intheevent B method and are substituted by events. Events modify the system state (or state variables), by executing an action, but if a guard holds. An event is not called but observed. When refining machines in classic B, one should maintain the number of op- erations both inthe abstract machine and inthe refinement; on the contrary, new events may be introduced inthe refinement model and they may modify only new variables. New events bring new proof obligations for ensuring a correct refinement. Finally, a B event-based model is a closed system with a finite list of state variables and a finite list of events. If the system reacts to its environment, theevent B model should integrate events of the environment. The B classical chapter introduces useful notations for theevent B method like set theory, generalised substitution, predicate calculus.
IRIT, Toulouse, France Sergei.Soloviev@irit.fr
Abstract. This paper studies how dependent types can be employed for a refined treatment of event types, offering a nice improvement to Davidson’s event semantics. We consider dependent event types indexed by thematic roles and illustrate how, inthe presence of refined event types, subtyping plays an essential role in semantic interpretations. We consider two extensions with dependent event types: first, the extension of Church’s simple type theory as employed in Montague semantics that is familiar with many linguistic semanticists and, secondly, the extension of a modern type theory as employed in MTT-semantics. The former uses subsumptive subtyping, while the latter uses coercive subtyping, to capture the subtyping relationships between dependent event types. Both of these extensions have nice meta-theoretic properties such as normalisation and logical consistency; in particular, we shall show that the former can be faithfully embedded into the latter and hence has expected meta-theoretic properties. As an example of applications, it is shown that dependent event types give a natural solution to the incom- patibility problem (sometimes called theevent quantification problem) in combining event semantics with the traditional compositional seman- tics, both inthe Montagovian setting with the simple type theory and inthe setting of MTT-semantics.
for fluence reaching 10 7 cm -2 . These positive results are
thought to be due to the doping of the epitaxial layer and the deep-well implants available and used in this technology, which prevents latchups. CIS1 devices are made using another process and are not immune to SELs. As can be seen in Fig. 17, CIS1 was studied in different operating modes. First, the device was biased and operated in nominal mode to take pictures. The number of SELs increases with LET, and the values can be fitted using the Weibull function. Several devices were irradiated to obtain this curve and provide a precise LET threshold of around 16 MeV. The threshold is higher than the maximum LET the protons can produce as a result of ionizing and by non-ionizing effects in silicon. However, layers of specific metals, such as copper and tungsten, are used in CIS leading to higher LET if the protons interact with these metals by displacement damage.
The present study follows the “ethnography of speaking” approach (Hymes 1972) to investigate the social and linguistic properties of an important formal eventinthe Eastern Maroon community, the kuutu ‘council meeting’. The data underlying this study were collected among the Pamaka maroons. My investigation shows that the kuutu event is characterized by structured social and linguistic practices that provide important face-saving strategies, and create an aura of dignity, importance and respectability. The social practices described here include participation privileges, and procedures for organizing and holding a kuutu. Concomitant linguistic practices include turn-taking procedures as well as lexical and pragmatic choices. The social conventions and speech acts described here are primarily associated with titled persons and elders, who are the sole active participants in a kuutu. The analysis provided also suggests that speech genre analysis offers important insights into the nature of linguistic varieties and the social meanings they index.
Novosibirsk State University, Novosibirsk, Russia
The temperature fluctuations generated by viscous dissipation in an isotropic turbulent flow are studied using direct numerical simulation. It is shown that their scaling with Reynolds number is at odds with predictions from recent investigations. The origin of the discrepancy is traced back to the anomalous scaling of the dissipation rate fluctuations. Phenomenological arguments are presented which explain the observed results. The study shows that previously proposed models underpredict the variance of frictional temperature fluctuationsby a factor proportional to the square of the Taylor-scale Reynolds number.
– [[Γ, P true]] = [[Γ ]], x : Prf([[P ]] Γ ), where x does not occur free in [[Γ ]]. The following theorem shows that the embedding is well-defined and faithful (inthe sense of the theorem) and hence C e has nice meta-theoretic properties (the corollary). Its proof is based on the embedding of Church’s simple type theory into the calculus of constructions [ 10 ]. We omit the discussion of technical details, for otherwise we would have to detail the syntax and rules of UTT and coercive subtyping [ 11 , 14 ], except remarking that a key reason that the proof goes through is because the coercions to model subtyping for dependent event types are constants and coherent (see Sect. 4.2 ) and hence model subsumptive subtyping in C e faithfully.
and v 5 to v 2 v 3 . Note that the last four-plane correla-
tor (Fig. 3(f)) is predicted to exceed unity when analyzed using the scalar-product method.
Conclusions.−We have argued that event-plane corre- lators in heavy-ion collisions can be analyzed with just two symmetric pseudorapidity windows. We have illus- trated the validity of our approach by analyzing events simulated within the AMPT model which reproduces for the first time the magnitude and centrality dependence of the measured correlators in Pb-Pb collisions at LHC. Much better agreement with data is achieved than in pre- vious hydrodynamic calculations using theevent-plane method [16, 17]. This apparent discrepancy between data and hydrodynamic calculations may simply be due to the ambiguity of theevent-plane method. It will then be re- solved once both experiment and theory switch from theevent-plane method to the scalar-product method. We have presented predictions for new correlators, in partic- ular large four-plane correlators, which can be measured in forthcoming analyses. It would be interesting to study the correlators using the procedure presented here intheevent-by-event hydrodynamical simulations to ascertain the sensitivity to initial-state models, namely the Monte- Carlo Glauber and the color-glass-condensate .
Grand Challenge Initiative. Using an incremental proof-based approach, we model functionalities of the Pacemaker. The approach is illustrated by developing a new formal model of the cardiac pacemaker system. Our contribution are in this report to model the single electrode pacemaker system using Event-B and prove it. The incremental proof-based devel- opment is mainly driven bythe refinement between an abstract model of the system and its detailed design through a series of refinements. A series of refinements is progressively added the functional and the timing prop- erties to the abstract system-level specifications using some intermediate models. The properties express system architecture, action-reaction and timing behavior. This paper uses all possible operational modes of a sin- gle electrode Pacemaker system that helps to develop better hardware. Every stage of refinement includes the detail information about oper- ating modes. The models are expressed inEvent-B modeling language and validated primarily bythe ProB tool in different situation such as hysteresis and rate adapting pacing under real-time constraints. In each stages of refinements include the detail information and more events are introduced. The final step of refinement completely localized the events and similar to implementation of single electrode pacemaker operating modes system. The stepwise refinement of the single electrode Pacemaker system contributes to achieve a high degree of automatic proof. Key words: Abstract model, Event-B, Event-driven approach, Proof- based development, Refinement, Pacemaker, Electrode, Heart