Formulation variationnelle pour le calcul de la diffraction d'une onde acoustique par une surface rigide

This work is a continuation of [1]. We give a space-time variational formula to the problem of the scattered acoutic wave by a hard body, using the double layer retarded potential technique. New schemes are constructed from this variationnal formula, for which we prove the stability and errors estimates.     

Li-ion batteries from LiFePO4 cathode and anatase/graphene composite anode for stationary energy storage

Li-ion batteries made from LiFePO₄ cathode and anatase TiO₂/graphene composite anode were investigated for potential application in stationary energy storage. Fine-structured LiFePO₄ was synthesized by a novel molten surfactant approach whereas anatase TiO₂/graphene nanocomposite was prepared via self-assembly method. The full cell that operated at 1.6 V demonstrated negligible fade even after more than 700 cycles at measured 1 C rate. While with relative lower energy density than traditional Li-ion chemistries interested for vehicle applications, the Li-ion batteries based on LiFePO₄/TiO₂ combination potentially offers long life and low cost, along with safety, all which are critical to the stationary applications.     

Graphs with prescribed mean curvature on hyperbolic spaces

We study a quasilinear elliptic equation in the unit ball ofℝ ^m . Using this result we get the existence of graphs with prescribed curvature on hyperbolic spacesℍ ^m inℍ ^m ×ℝ.     

Morse-Palais lemma for nonsmooth functionals on normed spaces

Using elementary differential calculus we get a version of the Morse-Palais lemma. Since we do not use powerful tools in functional analysis such as the implicit theorem or flows and deformations in Banach spaces, our result does not require the -smoothness of functions nor the completeness of spaces. Therefore it is stronger than the classical one but its proof is very simple.

     

The Mach reflection of shock waves in converging,cylindrical channels

Shock waves impinging on axisymmetric converging passages of moderate wall angle undergo cyclical Mach reflection processes which are generally not self-similar during progression through the contraction. This paper presents the results of shock tube experiments in air where shocks of moderate strength are incident on cones having a range of wall angles of 10° to 30°. Mach reflection is maintained as the dominant reflection process throughout this range but the number of cycles decreases as wall angle increases. A ray-shock approach, used to calculate the triple-point trajectories gives good agreement with the experimental locations of their intersections with the centreline and wall.     

Multi‐Species Multi‐Channel (MSMC): An Ab Initio‐based Parallel Thermodynamic and Kinetic Code for Complex Chemical Systems

Multi‐Species Multi‐Channel (MSMC) is an ab initio parallel program to calculate thermodynamic quantities (e.g., , , , and , time‐dependent species profiles, and rate coefficients as functions of temperature and pressure for complex chemical reaction systems, which consist of multiple stable species and multiple reaction channels interconnecting them. Thermodynamic properties of the species involved are calculated using statistical mechanics with molecular information from electronic structure calculations. Temperature‐ and pressure‐dependent behaviors are rigorously characterized within the eigenpair master equation/Rice–Ramsperger–Kassel–Marcus (ME/RRKM) framework. Corrections, e.g., for hindered internal rotation and tunneling treatment, are included. With the implementation of an ultra‐high precision package and rigorous matrix setup, MSMC is able to correctly mimic real behaviors of different types of chemical systems. Different eigenpair‐based approaches to extract phenomenological/macroscopic rate coefficients are implemented for different applications. Moreover, a friendly and platform‐independent graphical‐user‐interface (GUI) is provided to facilitate the use of MSMC and the pre‐/postcalculation data visualization/analysis on the fly. The program can be freely downloaded at https://sites.google.com/site/msmccode/ .