Eshelby’s solution-based homogenization procedures are often formulated from both Hill’s averages relations, equating the set average achieved over the mechanical strains (respectively stresses) of every inclusion constitut- ing the effective medium to the corresponding macro- scopic quantity (see relations (3) and (4) below). One can show that, when both of them are satisﬁed, the model is **self**-**consistent**, i.e., leads to the same macroscopic effective properties regardless of the equation used. Benveniste (1987) and several authors shown evidence that both Hill’s average relation could simultaneously be fulﬁlled by the Mori-Tanaka and **self**-**consistent** models, but at the cost of some restrictions over the materials microstructure: (i) either the inclusions must have the same Base Volume (BVs), i.e., shape and alignment of the elementary single heterogeneous inclusions accounted for achieving the **scale**-**transition** process should be strictly identical, (ii) or the material and inclusions must be isotropic, (iii) or only single or two-phase materials can be reliably modeled. This includes randomly oriented spheroidal particles, pen- ny-shaped particles randomly oriented in a layout, aligned ﬁbers in a composite ply, isotropic aggregates... Analytic expressions of the thermo-elastic macroscopic properties of the effective medium have been elegantly determined for these cases in a series of paper from Benveniste, Dvo- rak, and Chen (1991, 1992) . Some applications also can be found in Pham (2000) or Qiu and Weng (1991) .

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Marciniak and Kuczynski (1967) developed an approach based on the existence of an initial imperfection and coupled this localization criterion with an isotropic rigid-plastic constitutive framework in order to determine the right-hand side of the FLD. In most of the works devoted to the numerical prediction of FLDs, it is observed that both the shape and the location of these diagrams are extremely sensitive to the mechanical and physical properties. Accordingly, a wide range of phenome- nological behavior models have been coupled with various localization criteria to assess the in ﬂuence of some constitutive features, such as for instance strain-rate sensitivity ( Khan and Baig, 2011 ), plastic anisotropy ( Zhang and Wang, 2012 ), and damage-induced softening ( Haddag et al., 2009; Abed-Meraim et al., 2014; Mansouri et al., 2014 ). Despite their good pre- dictive capabilities, the phenomenological models, which are the most widely used for the prediction of FLDs, are not able to account for some essential physical and mechanical features, such as initial and induced textures and other microstructure- related parameters (grain morphology, crystallographic structure …). These limitations represent the main motivations behind the more recent use of micromechanical modeling for the FLD prediction. The advantage of such physically-based modeling, compared to phenomenological approaches, is its ability to link, in a natural way, the material microstructure to some important in-use properties (strength, formability …). Indeed, in micromechanical modeling, the constitutive relations are expressed at the single crystal level, and account for mechanisms relevant at this **scale** in the description of the hardening, such as the slip of crystallographic planes, lattice rotation, dislocation motion … The constitutive relations of the poly- crystalline aggregate are derived from those of its components (i.e., single crystals) on the basis of some **scale**-**transition** schemes. Therefore, prediction of FLDs based on micromechanical modeling requires three main ingredients: constitutive modeling at the **scale** of the single crystal, a multi-**scale** scheme to determine the mechanical behavior of the polycrystalline material, and a localization approach to predict the initiation of strain localization.

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a robust result, the change in V must therefore be associated to a change in the characteristic time, the latter then appearing as a key issue in under- standing and modeling turbulent transport. Finally the 1D model has been used to illustrate one of the possible problems that can be addressed in the κ-ε framework. Introducing in the definition of the velocity V a dependence on the shear of large **scale** flows, typically the zonal flows [44], so that the V exhibits a monotonic decrease from the low shear limit to the large shear limit, the ratio between these values being ≈ √ 2, we have reported in 1D simulations an H-mode like **transition** when increasing the input power, gen- erating an increased stored energy thanks to an interface barrier located at the separatrix [47]. This result is not quite a surprise since the predator-prey models have been introduced in fusion plasmas to investigate such barrier formation [41, 81, 46, 42]. Furthermore, the model has been devised to ex- hibit the appropriate trend, namely a decrease V with flow shear. However, the bifurcation aspect is not introduced specifically in the model. The tran- sition thus appears via a monotonic dependence of V on the shear completed by a feedback mechanism which governs a further increase of the flow shear as transport is reduced. This shows that the κ-ε model has the capability to generate changes of the transport regimes in a **self**-**consistent** manner.

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materials. In their work, a two-dimensional formulation has been adopted (i.e., the localization band is assumed to lie in the plane of the sheet). The same type of approach is followed in the current contribution, except that the **self**-**consistent** multi- **scale** model is used instead of the Taylor model. The motivation behind this choice of a two-dimensional formulation for the bifurcation criterion is to allow comparisons between the predicted FLDs and those yielded by the initial imperfection approach (which usually follows a two-dimensional formulation). Besides the development of very powerful and ef ﬁcient numerical tools for the prediction of ductility limits (which is, from the authors ’ perspective, an important originality in the current paper), we have also demonstrated another original result: when the initial imperfection ratio involved in the initial imperfection analysis tends towards zero, the associated FLDs tend towards the bifurcation-based FLD. It is noteworthy that this important result, which has already been demonstrated for phenomenological constitutive models (see, e.g., Ben Bettaieb and Abed-Meraim, 2015 ), is shown here to be valid for both **scale**-**transition** schemes, namely the Taylor model and the **self**- **consistent** scheme. Of course, such a comparison between the predictions given by the bifurcation theory and those yielded by the M eK analysis is not possible when the mechanical behavior is taken to be rate-dependent.

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1 Introduction
The thermal aging of polymers is a slow process occurring mainly on structural elements designed to experience mechanical loading, while being subjected to high temperatures for long periods. In many cases, matrix creep can occur. As the role of the matrices is essentially to deform and support stresses primarily in shear, it becomes then important to consider this particularity within a phenomenological modeling framework [4]. This context corresponds to the case of graphite- polyimide composites used in aerospace applications [1, 5]. According to, for instance, references [6, 7], below the glass **transition** temperature of its polymer matrix, composite materials exhibit a linear or at least a weakly nonlinear mechanical behavior until the damage threshold is attained. However, it is not the case anymore at high temperatures (relative to the glass **transition** temperature of the matrix). Indeed, recent experimental investigations performed at high temperatures on polyimide matrix composites, have shown very strong discrepancies from the linear elastic behavior [1, 2, 8]. These nonlinearities can be explained by two main mechanisms coupled together: the visco-elastic behviour of the polyimide matrix subjected to long-term loading at high temperatures, on the one hand, and the effects related to thermal aging, on the other hand.

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GeM, Institut de Recherche en Génie Civil et Mécanique, UMR CNRS 8163, Université de Nantes, Ecole Centrales de Nantes, CRTT, 37 Boulevard de l’Université, BP 406, 44602 Saint-Nazaire cedex, France
1 Introduction Metal forming processes require
knowledge of the evolution of the anisotropic elasto-plastic behaviour of the material during the deformation. Actually, the **scale** **transition** approach based on homogenisation techniques is currently used to predict the mechanical be- haviour of metallic materials at the macro- and micro- scopic levels [1, 2].

correlation content of the nuclear state. In this way, the mp-mh method allows to treat on the same footing long range correlations, beyond a mean-field that is improved as correlations are introduced. First multiconfiguration-type calculations based on Hartree-Fock single-particle states (as opposed to the usual oscillator sates) have been realized in e.g. [ 85 , 91 , 18 , 76 , 61 ]. The orbitals were however kept frozen. Pioneering work using the full Multi-Configuration **Self**-**Consistent** Field approach in the context of nuclear physics has been done a few decades ago [ 34 , 39 , 96 , 60 ]. However the applications performed in these studies were restricted to simple analytical cases (Lipkin model). The development of the multiparticle-multihole con- figuration mixing method at CEA,DAM,DIF started in the early 2000’s. So far, the studies that have been performed have not applied the full **self**-**consistent** formalism. Recent analysis of the spectroscopy of sd-shell nuclei using the Gogny interaction [ 86 , 63 ] used frozen Hartree- Fock orbitals, while an earlier work [ 84 ] applied the mp-mh method to the description of pairing correlations in Sn isotopes making drastic approximations in the equation determining the single-particle states. The goal of this thesis is to pursue the development of the mp-mh approach to be able to apply the full formalism to the description of nuclei. After formal and numerical developments, we are now able to exercise for the first time the completely **self**-**consistent** method to a few light nuclei. In particular, the first applications of this work are done for p and sd-shell nuclei using the Gogny interaction.

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permeability of vacuum, ~ j ext is current density of antenna, f i is distribution of resonant ion, C (f i ) is collision operator
and Q f i , ~ E is the quasi-linear operator of wave/particle interaction. To have a complete modelling, it is needed to take
account feedback of distribution on eld and inversely which means solving the two previous equations **self**-consistently. To solve the ICRF wave propagation (cf eq.1) we used the EVE code which is described in [19]. This full wave code calculates the wave electric eld by solving Maxwell's equations, using a variational principe. The quadratic dependence of the functional on the interaction Hamiltonian makes of EVE a second-order Finite Larmor Radius (FLR) code. The system of coordinates is (s, θ, ϕ), with s the radial coordinate, related to the poloidal ux by the relation ∇Ψ ≡ f (s) ∇s, and varying between 0 (centre) and 1 (edge) in the plasma volume. θ and ϕ are the poloidal and toroidal angles. The warm dielectric tensor in equation 1 is calculated assuming the heated distribution function is given by a bi-Maxwellian, i.e.

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Noting that these differences reflect those in the lo- cal symmetry of particles and their interactions, a third situation can be defined, intermediate between the po- lar ferromagnetic model and the apolar nematic one, that of **self**-propelled polar particles aligning nematically [12]. Such a mechanism is typically induced by volume exclusion interactions, when elongated particles collid- ing almost head-on slide past each other, as illustrated schematically in Fig. 1. Thus, **self**-propelled polar point particles with apolar interactions can be conceived as a minimal model for **self**-propelled rods interacting by in- elastic collisions [13, 14, 15]. Other relevant situations

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If we consider plasmas confined in tori, both for quasi-equilibria (including neoclassical transport theory) as well as for typical plasma instability phenomena in tor[r]

Bossert, Sprumont and Suzumura (2005a) have characterized all notions of rational- izability when the coherence property required is consistency. As mentioned earlier, con- sistency and transitivity are equivalent in the presence of reﬂexivity and completeness. Thus, greatest-element rationalizability by a reﬂexive, complete and **consistent** relation is equivalent to greatest-element rationalizability by an ordering and Richter’s (1966; 1971) results apply; see the next theorem. Moreover, greatest-element rationalizability by a complete and **consistent** relation implies greatest-element rationalizability by a reﬂexive, complete and **consistent** relation, and greatest-element rationalizability by a **consistent** re- lation implies greatest-element rationalizability by a reﬂexive and **consistent** relation, and analogous observations apply in the case of maximal-element rationalizability; see Bossert, Sprumont and Suzumura (2005a, Theorem 1). As pointed out in Bossert, Sprumont and Suzumura (2006), as soon as the coherence properties quasi-transitivity or acyclicity are imposed, reﬂexivity no longer is guaranteed as an additional property of a rationaliza- tion. Thus, consistency stands out from these alternative weakenings of transitivity in this regard: as is the case for transitive greatest-element (or maximal-element) rational- izability, any notion of **consistent** greatest-element (or maximal-element) rationalizability is equivalent to the deﬁnition that is obtained if reﬂexivity is added as a property of a rationalization.

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expressions g sc (x) can be analyzed in great detail, proving T
r < T < T l .
Acknowledgment. We thank Jonathan Mattingly and S.R.S. Varadhan for the help in the proof of the existence of the **self**-**consistent** profile. We also thank Herbert Spohn for useful discussions. The work of F. Bonetto was supported in part by NSF Grant DMS-060-4518, the work of J. L. Lebowitz was supported in part by NSF Grant DMR-044-2066 and by AFOSR Grant AF-FA 9550-04-4-22910, the work of J. Lukkarinen by Deutsche Forschungs- gemeinschaft (DFG) project SP 181/19-2 and by the Academy of Finland, the work of S. Olla by ANR LHMSHE no. BLAN07-2 184264 (France).

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/ La version de cette publication peut être l’une des suivantes : la version prépublication de l’auteur, la version acceptée du manuscrit ou la version de l’éditeur.. For the publisher[r]

S U M M A R Y
Progressive deformation of upper mantle rocks via dislocation creep causes their constituent crystals to take on a non-random orientation distribution (crystallographic preferred orien- tation or CPO) whose observable signatures include shear-wave splitting and azimuthal de- pendence of surface wave speeds. Comparison of these signatures with mantle flow models thus allows mantle dynamics to be unraveled on global and regional scales. However, existing **self**-**consistent** models of CPO evolution are computationally expensive when used with 3-D and/or time-dependent convection models. Here we propose a new method, called ANPAR, which is based on an analytical parametrization of the crystallographic spin predicted by the second-order (SO) **self**-**consistent** theory. Our parametrization runs ≈2–6 × 10 4 times faster

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Mots clés : choix rationnel, cohérence, domaines binaires
ABSTRACT
Consistency of a binary relation requires any preference cycle to involve indifference only. As shown by Suzumura (1976b), consistency is necessary and sufficient for the existence of an ordering extension of a relation. Because of this important role of consistency, it is of interest to examine the rationalizability of choice functions by means of **consistent** relations. We describe the logical relationships between the different notions of rationalizability obtained if reflexivity or completeness are added to consistency, both for greatest-element rationalizability and for maximal- element rationalizability. All but one notion of **consistent** rationalizability are characterized for general domains, and all of them are characterized for domains that contain all two-element subsets of the universal set.

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Mots clés : choix rationnel, cohérence, domaines binaires
ABSTRACT
Consistency of a binary relation requires any preference cycle to involve indifference only. As shown by Suzumura (1976b), consistency is necessary and sufficient for the existence of an ordering extension of a relation. Because of this important role of consistency, it is of interest to examine the rationalizability of choice functions by means of **consistent** relations. We describe the logical relationships between the different notions of rationalizability obtained if reflexivity or completeness are added to consistency, both for greatest-element rationalizability and for maximal- element rationalizability. All but one notion of **consistent** rationalizability are characterized for general domains, and all of them are characterized for domains that contain all two-element subsets of the universal set.

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ABSTRACT In this article we discuss the infrared properties of **self**-doped nanocrystals and in particular the case of HgSe. HgSe colloidal quantum dots have recently been reported for their tunable optical features all over the mid infrared from 3 to 20 µm. Their optical absorption is a combination of interband absorption at high energy and intraband absorption at low energy. The latter results from the **self**-doped character of HgSe. The origin of this **self**-doping is also discussed. We demonstrated that the doping results from the combination of the narrow band gap and high work function of HgSe, which leads to a reduction of the CQD by the water in the environment. In addition, we demonstrated that the doping density can be tuned over an order of magnitude thanks to the control of the capping ligands.

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Large-scale networked systems: from anarchy to geometric self-structuring Anne-Marie Kermarrec, Achour Mostefaoui, Michel Raynal, Gilles Trédan, Aline Viana.. To cite this version: Anne-[r]

We evaluate the algorithms along three metrics: i the number of rounds required to converge to a stabilized configuration; ii the reaction to load variations in term of number of created[r]

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•Baltes, P. B., & Baltes, M. M. (1990). Successful aging: Perspectives from the behavioral sciences. New York, NY : Cambridge University Press.
•Bouazzaoui, B., Isingrini, M., Fay, S., Angel, L., Vanneste, S., Clarys, D., & Taconnat, L. (2010). Aging and **self**-reported internal and external memory strategy uses: The role of executive functioning. Acta Psychologica, 135, 59-66 • Kliegel, M., & Zimprich, D. (2005). Predictors of cognitive complaints in older adults : A mixture regression approach. European Journal of Aging, 2(1), 13-23. • Marcotte, T. D., & Grant, I. (2010). Neuropsychology of everyday functioning. New York, NY: The Guilford Press.

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