Testing the Running of non-Gaussianity through the CMB mu-distortion and the Halo Bias

The primordial non-Gaussianity parameters fNL and tauNL may be scale-dependent. We investigate the capability of future measurements of the CMB mu-distortion, which is very sensitive to small scales, and of the large-scale halo bias to test the running of local non-Gaussianity. We show that, for an experiment such as PIXIE, a measurement of the mu-temperature correlation can pin down the spectral indices n_fNL and n_tauNL to values of the order of 0.3 if fNL = 20 and tauNL = 5000. A similar value can be achieved with an all-sky survey extending to redshift z ~ 1. In the particular case in which the two spectral indices are equal, as predicted in models where the cosmological perturbations are generated by a single-field other than the inflaton, then the 1-sigma error on the scale-dependence of the non-linearity parameters goes down to 0.2.Comment: 11 pages, 7 figure

Shock Structure in a Two-phase Isothermal Euler Model

We have performed a traveling wave analysis of a two phase isothermal Euler model to exhibit the inner structure of shock waves in two-phase flows. In the model studied in this work, the dissipative regularizing term is not of viscous type but instead comes from relaxation phenomena toward equilibrium between the phases. This gives an unusual structure to the diffusion tensor where dissipative terms appear only in the mass conservation equations. We show that this implies that the mass fractions are not constant inside the shock although the Rankine-Hugoniot relations give a zero jump of the mass fraction through the discontinuities. We also show that there exists a critical speed for the traveling waves above which no C 1 solutions exist. Nevertheless for this case, it is possible to construct traveling solutions involving single phase shocks

A numerical scheme for the computation of phase transition in compressible multiphase flows

International audienceThis paper is devoted to the computation of compressible multiphase flows involving phase transition. The compressible model is the system of Euler, without viscosity. For closing this model, an equation of state is required. In our context, the model of phase transition is included in the choice of the equation of state, via an entropy optimization of the mixture equation of state. Our aim is to simulate such a system, and for that, it is mandatory to understand well the Riemann problem with such an equation of state. We then propose a 2nd order numerical scheme, which is validated and proved to be accurate on one dimensional cases. Last, a 2D version of the code is proposed

A conservative method for the simulation of the isothermal Euler system with the van-der-Waals equation of state

International audienceIn this article, we are interested in the simulation of phase transition in compressible flows, with the isothermal Euler system, closed by the van-der-Waals model. We formulate the problem as an hyperbolic system, with a source term located at the interface between liquid and vapour. The numerical scheme is based on [1, 5]. Compared with previous discretizations of the van-der-Waals system, the novelty of this algorithm is that it is fully conservative. Its Godunov-type formulation allows an easy implementation on multidimensional unstructured meshes

Random integrals and correctors in homogenization

International audienceThis paper concerns the homogenization of a one-dimensional elliptic equation with oscillatory random coefficients. It is well-known that the random solution to the elliptic equation converges to the solution of an effective medium elliptic equation in the limit of a vanishing correlation length in the random medium. It is also well-known that the corrector to homogenization, i.e., the difference between the random solution and the homogenized solution, converges in distribution to a Gaussian process when the correlations in the random medium are sufficiently short-range. Moreover, the limiting process may be written as a stochastic integral with respect to standard Brownian motion. We generalize the result to a large class of processes with long-range correlations. In this setting, the corrector also converges to a Gaussian random process, which has an interpretation as a stochastic integral with respect to fractional Brownian motion. Moreover, we show that the longer the range of the correlations, the larger is the amplitude of the corrector. Derivations are based on a careful analysis of random oscillatory integrals of processes with long-range correlations. We also make use of the explicit expressions for the solutions to the one-dimensional elliptic equation

3D musculo-skeletal finite element analysis of the foot kinematics under muscle activation with and without ankle arthrodesis

International audienceThe choice between arthrodesis and arthroplasty in the context of advanced ankle arthrosis remains a highly disputed topic in the field of foot and ankle surgery. Arthrodesis, however, represents the most popular option. Biomechanical modeling has been widely used to investigate static loading of cadaveric feet as well as consequences of arthrodesis on bony structures. Although foot kinematics has been studied using motion analysis, this approach lacks accuracy in capturing internal joints motion due to limitations inherent to external “marker sets” and the fact that it imposed the foot to be considered as a rigid solid. The consequences of arthrodesis on kinematics of the unloaded foot are not well understood although it is of crucial importance during the swing phase and at heel contact. Investigating ankle mobility during muscle contraction with and without arthrosis could explain how the motion is produced by extrinsic muscles activations affected by an arthrodesis. This study aims at defining if a biomechanical model with Finite Elements could help arthrodesis understanding

Runge-Kutta discontinuous Galerkin method for reactive multiphase flows

International audienceA Runge-Kutta discontinuous Galerkin method is developed for the model- ing of reactive compressible multiphase flows. From the work developed in [1], where a discontinuous Galerkin formulation was obtained for inert flows based on the ideas of [2] and [3], we introduce a reactive Riemann problem [4] so as to take into account the reactions we are interested in (i.e. reactions with infinitely fast time rates). Several reactive examples are presented. The corresponding results show the high capabilities of the method, which can simulate the strong density and pressure ratios, and also has no problem whenever a phase appears or disappears

A low Mach correction able to deal with low Mach acoustic and free of checkerboard modes

National audienceIt is well known that finite volume schemes are not accurate at low Mach number in the sense that they do not allow to obtain the incompressible limit when the Mach number is small on Cartesian meshes [4]. Increase the order of the method with a Discontinous Galerkin method is not sufficient to get the accuracy at low Mach number [1]. The schemes needs corrections [4, 5, 3, 2]. These corrections aim at reducing the numerical diffusion of the scheme to obtain accurate schemes for flows near the incompressible limit but could induce checkerboard modes [5, 2]. Moreover, since this diffusion is necessary to stabilize the scheme, it is also interesting to focus on the accuracy of the scheme at low Mach number with respect to the acoustic part of the solution. We will present a corrected scheme that is accurate at low Mach number for steady and unsteady flows, has the same CFL restriction as the Roe scheme for an explicit time integration and is free of checkerboard modes

Derivation and Closure of Baer and Nunziato Type Multiphase Models by Averaging a Simple Stochastic Model

International audienceIn this article, we show how to derive a multiphase model of Baer and Nunziato type with a simple stochastic model. Baer and Nunziato models are known to be unclosed, namely, they depend on modeling parameters, as interfacial velocity and pressure, and relaxation terms, whose exact expression is still an open question. We prove that with a simple stochastic model, interfacial and relaxation terms are equivalent to the evaluation of an integral, which cannot be explicitly computed in general. However, in different particular case matching with a large range of applications (topology of the bubbles/droplets, or special flow regime conditions), the interfacial and relaxation parameters can be explicitly computed, leading to different models that are either nonlinear versions or slight modifications of previously proposed models. The validity domains of previously proposed models are clarified, and some modeling parameters of the averaged system are linked with the local topology of the flow. Last, we prove that usual properties like entropy dissipation are ensured with the new closures found