Optical corrosion meter

In a previous study, a mathematical model relating surface and bulk behaviours of metals in aqueous solution has been developed. The model was established based on principles of holographic interferometry for measuring microsurface dissolution, i.e. mass loss, and on those of electrochemistry for measuring the bulk electronic current, i.e. corrosion current. In the present work, an optical corrosion meter was built based on the above model. The corrosion meter consists of an electrochemical cell in which the sample is immersed in aqueous solution. Furthermore, the corrosion meter has a holographic camera with a thermoplastic film for in situ processing of holograms in order to obtain real-time holographic interferoms of the sample in the electrochemical cell. Results of the present work indicate that optical holography is a very useful technique for measuring the corrosion current density of different alloys in aqueous solutions. As a result, the corrosion current density of aluminium, stainless steel, and low-carbon steel in 1 M KCl, 1 M NaCl, and 1 M NaOH solutions were obtained. A comparison between the corrosion data of samples showed that the corrosion current density of the stainless steel in 1 M NaCl is nearly three-folds higher than that of the aluminium in 1 M KCl and the low-carbon steel in 1 M NaOH.     

Lagrangian flows: The dynamics of globally minimizing orbits

The objective of this note is to present some results, to be proved in a forthcoming paper, about certain special solutions of the Euler-Lagrange equations on closed manifolds. Our main results extend to time dependent periodic Lagrangians with minor modifications.We have chosen the autonomous case because this formally simpler framework allows to reach more easily the core of our concepts and results. Moreover the autonomous case exhibits certain special features involving the energy as a first integral that deserve special attention. They are closely related to the link found by Carneiro [C] between the energy and Mather's action function [Ma].Reprinted by permission of Addison Wesley Longman Ltd.     

New critical dimensions forq-deformed bosonic string

Applying the mass shell condition forq-deformed open and closed strings, new critical space-time dimensions are derived. Supported by the Algerian Ministry of High Education and Research under contract N^oD2501/17/01/93. Permanent address.     

The gas dynamics of current-limiting devices during immobility time

The aim of this paper is to extend our knowledge about the gas-dynamic processes in arcs during immobility time. For this purpose, the conservation equations in a magnetohydrodynamic approximation were coupled with the thermochemical and Maxwell equations. Special features arc the introduction of dissociation and ionization of nitrogen and oxygen, and the simultaneous calculation of the distributions of current density and magnetic induction in the arc. Numerical calculations were performed with a reduced two-dimensional (2-D) time-dependent model. Results of the calculations were compared with measurements. The development in time of the measured and calculated are voltage and arc chamber pressure show very good agreement. The pumping effect of the double vortex in the arc region was confirmed by optical measurements. It is concluded that the three-layer model is a good representation for the main physical features during the immobility time, and that the presence of highly conducting gas in the downstream region of the arc is essential for its downstream movement     

Variational treatment for the dynamical pseudo Jahn-Teller system

We present a variational treatment for the E × e pseudo Jahn-Teller system. Through canonical transformation the electron and phonon states are decoupled. An analytical form is obtained for the ground state energy by scaling transformation. Including both the dynamical displacement of phonon modes and the softening of phonon frequency, this approach yields fairly accurate results for the ground state energy. The energy splitting and Ham's reduction factor are calculated, which also generates fairly good results compared with other perturbation results. We argue that our variational wave function is valid for the weak and intermediate coupling range.     

Classical versus Jennings model for the ground state of H near a metallic surface

We show that, contrary to earlier reports, application of the one-parameter variational technique to the classical (image) model for H in front of an Al surface leads to energy shifts for the ground state which are very close to those obtained numerically with a more sophisticated model of the system.     

Diffusing particles with electrostatic repulsion

Summary. We study a diffusion model of an interacting particles system with general drift and diffusion coefficients, and electrostatic inter-particles repulsion. More precisely, the finite particle system is shown to be well defined thanks to recent results on multivalued stochastic differential equations (see [2]), and then we consider the behaviour of this system when the number of particles goes to infinity (through the empirical measure process). In the particular case of affine drift and constant diffusion coefficient, we prove that a limiting measure-valued process exists and is the unique solution of a deterministic PDE. Our treatment of the convergence problem (as ) is partly similar to that of T. Chan [3] and L.C.G. Rogers - Z. Shi [5], except we consider here a more general case allowing collisions between particles, which leads to a second-order limiting PDE. Received: 5 August 1996 / In revised form: 17 October 1996