Search results for "solution"

Zero viscosity limit of the Oseen equations in a channel

2001

Oseen equations in the channel are considered. We give an explicit solution formula in terms of the inverse heat operators and of projection operators. This solution formula is used for the analysis of the behavior of the Oseen equations in the zero viscosity limit. We prove that the solution of Oseen equations converges in W1,2 to the solution of the linearized Euler equations outside the boundary layer and to the solution of the linearized Prandtl equations inside the boundary layer. © 2001 Society for Industrial and Applied Mathematics.

Primary and secondary distributions after a small-amplitude potential step at disk electrode coated with conducting film

2011

Abstract The set of equations and boundary conditions for the “primary potential/current distribution” after a small-amplitude potential step has been analyzed for a film-coated disk electrode in contact with an electrolyte. The solution of these equations provides the overall short-time resistance of this system, Rtot, which is determined by the short-time resistance of the electrolyte solution in contact with the bare disk electrode, Rs, and the short-time film resistance to the current passage in the normal direction, R f = L f / κ f π r o 2 (ro, disk radius; Lf, film thickness; κf, its specific conductivity). The deviation of Rtot from the sum of these resistances, Rs + Rf, originates f…

Acid versus base peptization of mesoporous nanocrystalline TiO2 films: functional studies in dye sensitized solar cells

2005

We report an analysis of the influence of acid/base conditions employed in the synthesis of TiO2 nanoparticles upon the performance of dye sensitised photoelectrochemical solar cells fabricated from these particles. The functional properties of the TiO2 nanoparticles in these devices are investigated by potential step chronoamperometry, transient laser spectroscopy, and photovoltaic device characterisation. We find that base peptization conditions employed in the sol–gel fabrication of the TiO2 nanoparticles result in a reduction in film electron density under negative applied bias, correlated with slower interfacial recombination losses and a higher device open circuit voltage.

ON THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION WITH A QUASI-PERIODIC POTENTIAL

1980

Some exact solutions of the two dimensional Bussinesq equation

2010

Rôle des espèces sulfures dans la corrosion des aciers non alliés : hétérogénéités de la couche de produits de corrosion et couplages galvaniques

2014

The present study relates to the problem of the long-term interim storage of nuclear wastes. In France, it is envisaged that high-level radioactive wastes will be confined in a glass matrix, stored in a stainless steel canister, itself placed in a carbon steel overpack. The wastes will then be stored at a depth of ~450 m in a deep geological disposal, drilled in a very stiff (indurated) clay (argillite) formation. A temperature as high as 90°C is expected at the steel surface because of the intense radioactivity. Anodic polarization at applied current density was used to synthetize corrosion product layers likely to be formed in storage conditions. The S235 steel electrodes were covered by …

Modified Landau levels, damped harmonic oscillator and two-dimensional pseudo-bosons

2010

In a series of recent papers one of us has analyzed in some details a class of elementary excitations called {\em pseudo-bosons}. They arise from a special deformation of the canonical commutation relation $[a,a^\dagger]=\1$, which is replaced by $[a,b]=\1$, with $b$ not necessarily equal to $a^\dagger$. Here, after a two-dimensional extension of the general framework, we apply the theory to a generalized version of the two-dimensional Hamiltonian describing Landau levels. Moreover, for this system, we discuss coherent states and we deduce a resolution of the identity. We also consider a different class of examples arising from a classical system, i.e. a damped harmonic oscillator.

Evaluation of advanced silica packings for the separation of biopolymers by high-performance liquid chromatography

1989

Abstract The linear solvent strength model of Snyder was applied to describe fast protein separations on 2.1-μm non-porous, silica-based strong anion exchangers. It was demonstrated on short columns packed with these anion exchangers that (i) a substantially higher resolution of proteins and nucleotides was obtained at gradient times of less than 5 min than on porous anion exchangers; (ii) the low external surface area of the non-porous anion exchanger is not a critical parameter in analytical separations and (iii) μg-amounts of enzymes of high purity and full biological activity were isolated.

Efficient Resolution of Menthylamine with Inexpensive (R,R)-Tartaric Acid by Dielectrically Controlled Resolution (DCR)

2013

A practical procedure for the resolution of menthylamine 2 with (R,R)-tartaric acid [(R,R)-3] as resolving agent is presented. Variation of the solvent system allows both enantiomers of 2 to be selectively crystallized. Performing the resolution in methanol containing 6 % water leads to (–)-2·(R,R)-3·MeOH. The other, less-soluble diastereomeric salt is obtained by applying a solvent system consisting of methanol with 19 % water with a yield of 14 %. Subsequent basic workup with aqueous sodium hydroxide gave the free menthylamine compounds. Further workup of the mother liquors and an additional recrystallization step allowed the (–)-2·(R,R)-3·MeOH salt to be obtained in an overall yield of 2…

Microscopic aspects of solute-solute interactions induced by the solvent

1996

Nous presentons les plus importants resultats que nous ayons obtenus par des simulations etendues de dynamique moleculaire de solutions aqueuses contenant des modeles de solute hydrophiles et hydrophobes. Ces simulations determinent les forces induites par le solvant sur les solutes (SIFs) en fonction du type de solute, de la separation solute-solute et de leur orientation mutuelle. Les proprietes structurales et dynamiques du solvant autour des solutes ont ete analysees pour comprendre leur relation avec les SIFs. les presents resultats sont compares a des observations experimentales et precedentes stimulations sur des solutions aqueuses de biomolecules.