On the self-similar solution to the Euler equations for an incompressible fluid in three dimensions

The equations for a self-similar solution to an inviscid incompressible fluid are mapped into an integral equation that hopefully can be solved by iteration. It is argued that the exponents of the similarity are ruled by Kelvin's theorem of conservation of circulation. The end result is an iteration with a nonlinear term entering a kernel given by a 3D integral for a swirling flow, likely within reach of present-day computational power. Because of the slow decay of the similarity solution at large distances, its kinetic energy diverges, and some mathematical results excluding non-trivial solutions of the Euler equations in the self-similar case do not apply.     

Data assimilation and pollution forecasting in Burgers' equation with model error function

This article presents a correction method for a better resolution of the problem of estimating and predicting pollution, governed by Burgers' equations. The originality of the method consists in the introduction of an error function into the system's equations of state to model uncertainty in the model. The initial conditions and diffusion coefficients, present in the equations for pollution and concentration, and also those in the model error equations, are estimated by solving a data assimilation problem. The efficiency of the correction method is compared with that produced by the traditional method without introduction of an error function.Three test cases are presented in this study in order to compare the performances of the proposed methods. In the first two tests, the reference is the analytical solution and the last test is formulated as part of the “twin experiment”.The numerical results obtained confirm the important role of the model error equation for improving the prediction capability of the system, in terms of both accuracy and speed of convergence.     

Homogenization of Periodically Heterogeneous Thin Beams

Consider an elastic thin three-dimensional body made of a periodic distribution of elastic inclusions. When both the thickness of the beam and the size of the heterogeneities tend simultaneously to zero the authors obtain three different one-dimensional models of beam depending upon the limit of the ratio of these two small parameters.     

An investigation of paddle wheel Cu2(μ2-O2CCH3)4 for gas molecule adsorptions

Metal organic frameworks (MOFs) have been well-known and extensively researched due to the high storage /good selectivity for gas molecules. Herein, the structures and electron paramagnetic resonance (EPR) spectra for dicopper paddle wheel MOF compound (Cu₂(µ₂-O₂CCH₃)₄ with various gas molecule are theoretically investigated by density functional theory (DFT) calculations. The adsorption energies and isotherms (including pure gas molecules and the mixed ones) are calculated for the gas molecules interacting with the unsaturated Cu₂(µ₂-O₂CCH₃)₄. Both quantities exhibit the roughly consistent orders (e.g. H₂S?>?NH₃?>?CO₂?>?CO?>?H₂O?>?N₂?>?NO?>?H₂ for isotherms and H₂S?>?NH₃?>?N₂?>?CO₂?>?NO?>?H₂O?>?H₂?>?CO for adsorption energies), possibly suggesting that this material may act as a potential adsorbent of these gas molecules. The catalytic property of Cu₂(µ₂-O₂CCH₃)₄ for oxidation of CO and NO into non-toxic molecules and splitting of H₂O into H₂ and O₂ in the solvent condition are uniformly discussed. Simulation of Grand Canonical Monte Carlo (GCMC) in MS 8.0 and calculations in Langmuir model reveal that Cu₂(µ₂-O₂CCH₃)₄ has good selectivity for CH₄ in natural gas (CH₄/CO₂/N₂) and SO₂ in fog (SO₂/NO/NO₂/H₂O/O₂), which would exhibit potential environmentally friendly applications.     

Study of the performances of an oxygen carrier: Experimental investigation of the binder's contribution and characterization of its structural modifications

The aim of this work is to investigate the contribution of the binder (NiAl₂O₄) on the performances of the oxygen carrier NiO/NiAl₂O₄. To this purpose, oxidation/reduction cycles have been performed in a fixed bed reactor using CO as a fuel. The results reveal that the binder can react with the fuel to form CO₂, and that its total reduction capacity increases with temperature. XRD characterizations performed on the binder (on the fresh and after several cycles) show a shift of the diffraction peaks of NiAl₂O₄ toward the ones of γ-alumina, which can be attributed to a progressive decomposition of NiAl₂O₄ to alumina and NiO.     

The stochastic energy-Casimir methodLa méthode d'énergie-Casimir stochastique

In this paper, we extend the energy-Casimir stability method for deterministic Lie–Poisson Hamiltonian systems to provide sufficient conditions for stability in probability of stochastic dynamical systems with symmetries. We illustrate this theory with classical examples of coadjoint motion, including the rigid body, the heavy top, and the compressible Euler equation in two dimensions. The main result is that stable deterministic equilibria remain stable in probability up to a certain stopping time that depends on the amplitude of the noise for finite-dimensional systems and on the amplitude of the spatial derivative of the noise for infinite-dimensional systems.