A memory‐efficient finite volume method for advection‐diffusion‐reaction systems with nonsmooth sources

We present a parallel matrix‐free implicit finite volume scheme for the solution of unsteady three‐dimensional advection‐diffusion‐reaction equations with smooth and Dirac‐Delta source terms. The scheme is formally second order in space and a Newton–Krylov method is employed for the appearing nonlinear systems in the implicit time integration. The matrix‐vector product required is hardcoded without any approximations, obtaining a matrix‐free method that needs little storage and is well‐suited for parallel implementation. We describe the matrix‐free implementation of the method in detail and give numerical evidence of its second‐order convergence in the presence of smooth source terms. For nonsmooth source terms, the convergence order drops to one half. Furthermore, we demonstrate the method's applicability for the long‐time simulation of calcium flow in heart cells and show its parallel scaling. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq31: 143–167, 2015     

Diffraction problems with impedance conditions

The two- or three-dimensional electromagnetic diffraction problem for a half-plane impedance or reactance sheet belongs to a class of elliptic transmission problems of mixed type. Sobolev spaces of order 1 and ±1/2 are naturally involved according to the energy norm and the trace theorem, respectively. This operator theoretic approach presents the equivalence to systems of Wiener-Hopf equations and their solution in the sense of a well-posed problem with respect to the spaces under consideration. Slightly different impedance numbers for the two banks of the screen lead to a perturbation problem. All results yield direct a priori estimates for the solutions.     

The effective dielectric constant of plasmas — A mean field theory built from the electromagnetic ionic T-matrix

This work aims to obtain the effective dielectric constant tensor of a warm plasma in the spirit of the derivation of a mixing law. The medium is made of non point-like ions immersed in an electron gas with usual conditions relating the various lengths which define the problem. In this paper the ion dielectric constants are taken from their RPA responses as developed in a previous paper [1]. Furthermore the treatment of the screening effects is made through a mathematical redefinition of the initial problem as proposed in Ref. [1]. Here the complete calculation of the T-matrix describing the scattering of an electromagnetic wave on an isolated ion immersed in an “effective medium” is given. It is used for building , in the spirit of a mixing law, a self-consistent effective medium theory for the plasma dielectric tensor. We then extend the results obtained in Ref. [1] to higher orders in ion or dielectric inclusion densities. The techniques presented are generic and can be used in areas such as elasticity, thermoelasticity, and piezoelectricity.     

Electron spin resonance study of radicals generated in cellulose/N-methylmorpholine solutions after flash photolysis at 77 K

The processes of radical formation in N-methylmorpholine-N-oxide monohydrate (NMMO) and cellulose/NMMO solutions were studied by ESR at 77 K under high-power UV (lambda = 248 nm) excimer laser flash photolysis. Radicals mainly generated were attributed to the nitroxide type radicals -CH2-NO*-CH2- and -CH2-NO*-CH3 at the first step and methyl *CH3 and formyl *CHO radicals at the second step of the photoreaction. Kinetic studies of these radicals revealed that formation and recombination rates of the radicals depend on the cellulose concentration in cellulose/NMMO solutions and the concentration of additional ingredients, e.g. Fe(II) and propyl gallate. Even at frozen state temperature, acceleration or quenching of radical reaction processes was found. The proposed scheme of UV light-induced NMMO degradation during irradiation based on ESR data correlates well with independently obtained results based on high-performance liquid chromatography (HPLC). The analysis of degradation products by HPLC, e.g. aminoethanol and acetaldehyde, supports the assumption concerning a radical-initiated ring opening of NMMO.     

Cascaded optical parametric oscillation with a dual-grating periodically poled lithium niobate crystal

We demonstrate continuous-wave cascaded optical parametric oscillation in which the signal field of the primary parametric oscillator internally pumps the secondary parametric oscillator. Wavelength tuning is achieved with temperature tuning and a fan-out grating structure of a dual-grating periodically poled lithium niobate crystal. Above the secondary threshold the primary signal power is clamped, and all the other output powers increase linearly with the input pump power, in accordance with theory. Cascaded parametric oscillation offers a convenient and efficient way to generate multiple tunable outputs.     

Choosing norms in adaptive FSI calculations

The thermal coupling of a fluid and a structure is of great significance for many industrial processes. As a model for cooling processes in heat treatment of steel we consider the coupling of the compressible Navier-Stokes equations along a surface with the heat equation. A partitioned approach is considered, where different codes for the sub-problems are employed. We use a finite volume method (FVM) for the fluid and a finite element method (FEM) for the heat equation. The semi-discrete coupled system is solved using stiffly stable SDIRK methods, where on each stage an FSI problem is solved. This has a black box character, since a stage calculation corresponds to a specific Backward-Euler integration step. For the resulting method it was shown by numerical experiments in [1] that second order convergence rate is obtained. This property is used for a simple time-step control, which saves considerable computational time and guarantees a specified maximum error of time integration. Here, we will consider different norms for measuring the error. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

From the dilute solution to the pure compound: Extraction strategy based on a multi-stage process of phase separation

It is very rare that a one-step process of extraction leads to the pure compound with a high degree of purity specified by an industrial application. The various stages of a synthesis process and possible secondary reactions may lead to the synthesis of more or less complex and highly diluted solutions. In this work, the rationale and strategy for extraction and purification of a high added value compound are discussed. All the thinking is based on the knowledge and the exploitation of phase diagrams and then developed for different unit operations of the process. The most significant research tools are the experimental data and the modelling of phase equilibrium to estimate the yield of each step of extraction. The significant example chosen involves all the basic methods of phase separation, starting with liquid-vapour equilibrium: stripping of high volatility components and then more or less complex distillation are classically employed. The theoretical plateau number can be deduced from the equilibrium equation curves. The second step is based on the study of the liquid-liquid equilibrium and is an intermediate step for enrichment of the solution when distillation is not possible. A final step based on solid-liquid equilibrium consists of the selective crystallization of the pure product at low temperature, in order to satisfy the requirements of purity and safety imposed by industrial use. The conclusion includes all isolation operations in the form of a general extraction and purification scheme.

     

On The Curvature of the Real Milnor Fiber

Let C be a germ at O R² of a real analytic plane curve, andC^C its complexification; let C_t B be a fiber of a real smoothdeformation of C in the ball B = B(O,). The following inequalityis proved between the integrals of real curvature k of C_t andthose of Gaussian curvature K of : The sharpness of this inequality is proved in the case whereC is a real irreducible germ. Similar results are proved foran affine algebraic curve C R² of degree d. 2000 MathematicsSubject Classification 14H20, 14H50, 53A04.     

Décomposition du percarbonate de O,O-t-butyle et O-isopropényle en solution: Acétonylation des esters,acides et nitriles

The Free-Radical Decomposition of O,O-t-Butyl and O-Isopropenyl Peroxycarbonate in Solution: the Acetonylation of Esters, Acides and Nitriles The free-radical decomposition of O, O-t-butyl and O-isopropenyl peroxycarbonate in substratres possessing mobile H-atoms (S? H) consists mainly in an induced chain process leading to acetonylated derivatives of the solvent. Fairly good yields are obtained but teh acetonylation of functional substrates often gives mixtures of isomers. In the case of methyl acetate, the acetonylation occurs on the C-atoms adjacent to the carbonyl (acylox moiety) and to the O-atom (alkox moiety). However, the relative amounts of the isomeric products depend on the concentration of the peroxycarbonate solutions; at lowest concentration, methyl 4-oxopentanoate (acyloxy moiety) is obtained selectively. It is assumed that the free radicals issued from the solvent are able to abstract H-atoms of other molecules of solvent before adding to the double bond of the peroxycarbonate; the more the peroxycarbonate solution is diluted the more the transfers from the C-atom adjacent to the carbonyl to the radicals adjacent to the O-atom are favoured. In the case of methyl alkanoates, H-transfers from the α-C-atoms to β-radicals of teh acyloxy moiety may account for the orientation of the process. Owing to similar H-transfer processes, the acetonylation of functional esters, of acids and nitriles is selective in most cases.