Wall-Resolved Large Eddy Simulations of the Transient Turbulent Fluid Mixing in a Closed System Replicating a Pressurized Thermal Shock

The isothermal mixing of a heavy and a light liquid of different physical properties is numerically investigated by means of Large Eddy Simulations. The validation is based on experimental data held in a system reproducing various components of a pressurized water nuclear reactor, during a scenario of cold water injection at a low Atwood number of 0.05. The flow has two distinct stages: first a buoyancy-driven phase is characterized by a fluid front development in the cold leg and gives rise to Kelvin–Helmholtz whorls under the action of density changes. Then, the heavy liquid discharges into the downcomer filled with light liquid, which causes a turbulent mixing. These phenomena are analyzed through a single-phase approach where the density of the working fluid is either variable or modeled by the Boussinesq approximation. The influence of grid refinement is deeply examined, which shows that the mesh convergence is well achieved for the main flow quantities, unlike the low-magnitude spanwise components. Overall, the numerical solutions are found to reproduce the experimental measurements with a fair accuracy for both physical models used. These latter exhibit similar trends, due to the small density difference under consideration. The predictions in the downcomer appear to be more challenging owing to a strongest turbulence than in the cold leg, some flow features being not properly captured. However, the experimental data in the downcomer are found to be incomplete and somewhat dubious for a strict validation of the numerical simulations. Lastly, the flow distribution in the dowcomer is investigated, providing further insight on the mixing process.

     

Convergence to equilibrium in competitive Lotka–Volterra and chemostat systems

We study a generalized system of ODE's modeling a finite number of biological populations in a competitive interaction. We adapt the techniques in Jabin and Raoul [8] and Champagnat and Jabin (2010) [2] to prove the convergence to a unique stable equilibrium.     

A mathematical model of immune competition related to cancer dynamics

This paper deals with the qualitative analysis of a model describing the competition among cell populations, each of them expressing a peculiar cooperating and organizing behavior. The mathematical framework in which the model has been developed is the kinetic theory for active particles. The main result of this paper is concerned with the analysis of the asymptotic behavior of the solutions. We prove that, if we are in the case when the only equilibrium solution if the trivial one, the system evolves in such a way that the immune system, after being activated, goes back toward a physiological situation while the tumor cells evolve as a sort of progressing travelling waves characterizing a typical equilibrium/latent situation. Copyright © 2009 John Wiley & Sons, Ltd.     

Clustering and asymptotic behavior in opinion formation

We investigate the long time behavior of models of opinion formation. We consider the case of compactly supported interactions between agents which are also non-symmetric, including for instance the so-called Krause model. Because of the finite range of interaction, convergence to a unique consensus is not expected in general. We are nevertheless able to prove the convergence to a final equilibrium state composed of possibly several local consensus. This result had so far only been conjectured through numerical evidence. Because of the non-symmetry in the model, the analysis is delicate and is performed in two steps: First using entropy estimates to prove the formation of stable clusters and then studying the evolution in each cluster. We study both discrete and continuous in time models and give rates of convergence when those are available.     

Locally normal subgroups of simple locally compact groups

We announce various results concerning the structure of compactly generated simple locally compact groups. We introduce a local invariant, called the structure lattice, which consists of commensurability classes of compact subgroups with open normaliser, and show that its properties reflect the global structure of the ambient group.     

Identification of the Dilute Regime in Particle Sedimentation

We investigate the dynamics of rigid, spherical particles of radius R sinking in a viscous fluid. Both the inertia of the particles and the fluid are neglected. We are interested in a large number N of particles with average distance dR. We investigate in which regime (in terms of N and R/d) the particles do not significantly interact and approximately sink like single particles. We rigorously establish the lower bound for the critical number N_crit of particles. This lower bound agrees with the heuristically expected N_crit in terms of its scaling in R/d. The main difficulty lies in showing that the particles cannot get significantly closer over a relevant time scale. We use the method of reflection for the Stokes operator to bound the strength of the particle interaction.     

Synthesis and conformational study of the first triply bridged calix[6]azatubes

[reaction: see text] The first C(3)(v)- and D(3)(h)-symmetrical triply bridged calix[6]azatubes were prepared in good yields from the known 1,3,5-tris-methylated calix[6]arene through an efficient [1 + 1] macrocyclization reaction. A remarkably regioselective hexa ipso-nitration reaction led to a calix[6]azatube substituted at the wide rim in alternate position by tBu and nitro groups. A (1)H NMR study showed that, whereas the parent bis-calix[6]arenes self-include their methoxy groups, thereby closing their inner tube, the nitro-substituted calix[6]azatube undergoes a conformational change with the expulsion of the methoxy groups, hence presenting a three-dimensional structure open for host-guest applications.     

Palladium-catalyzed borylation of phenyl bromides and application in one-pot Suzuki-Miyaura biphenyl synthesis

The coupling reaction of pinacolborane with various aryl bromides in the presence of a catalytic amount of Pd(OAc)(2) together with DPEphos as ligand and Et(3)N as base provided arylboronates. High yields were obtained in the case of electron-donor substituted aryl bromides. The direct preparation of arylboronates allowed the one-pot, two-step synthesis of unsymmetrical biaryls in high yields. [reaction: see text]     

Orienting the Pore Morphology of Core-Shell Magnetic Mesoporous Silica with the Sol-Gel Temperature. Influence on MRI and Magnetic Hyperthermia Properties

The controlled design of robust, well reproducible, and functional nanomaterials made according to simple processes is of key importance to envision future applications. In the field of porous materials, tuning nanoparticle features such as specific area, pore size and morphology by adjusting simple parameters such as pH, temperature or solvent is highly needed. In this work, we address the tunable control of the pore morphology of mesoporous silica (MS) nanoparticles (NPs) with the sol-gel reaction temperature (T_sg). We show that the pore morphology of MS NPs alone or of MS shell covering iron oxide nanoparticles (IO NPs) can be easily tailored with T_sg orienting either towards stellar (ST) morphology (large radial pore of around 10 nm) below 80 °C or towards a worm-like (WL) morphology (small randomly oriented pores channel network, of 3–4 nm pore size) above 80 °C. The relaxometric and magnetothermal features of IO@STMS or IO@WLMS core shell NPs having respectively stellar or worm-like morphologies are compared and discussed to understand the role of the pore structure for MRI and magnetic hyperthermia applications.