Champ de vitesse dans un échangeur à vortex en régime turbulentHeat exchanger velocity field with turbulent inlet condition

We consider the isothermal flow through a cylindrical flat chamber, a model of some particular heat exchanger, for which LDV measurements and a numerical simulation have been performed. Experimental results show the establishment of an important vortex zone, the secondary flow extending all along the chamber radius. This observation leads to an expected significant increase of the fluid mixing. Results issued from the numerical simulation appear to be in close agreement with experimental data. Nevertheless, the k–ε model used here must be improved to obtain a better approach near the vortex centre. To cite this article: S. Petitot et al., C. R. Mecanique 330 (2002) 593–599.     

The (1+1) Dimensional Dirac Equation With Pseudoscalar Potentials: Path Integral Treatment

The supersymetric path integrals in solving the problem of relativistic spinning particle interacting with pseudoscalar potentials is examined. The relative propagator is presented by means of path integral, where the spin degrees of freedom are described by odd Grassmannian variables and the gauge invariant part of the effective action has a form similar to the standard pseudoclassical action given by Berezin and Marinov. After integrating over fermionic variables (Grassmannian variables), the problem is reduced to a nonrelativistic one with an effective supersymetric potential. Some explicit examples are considered, where we have extracted the energy spectrum of the electron and the wave functions. PACS numbers: 03.65. Ca-Formalism, 03.65. Db-Functional analytical methods, 03.65. Pm-Relativistic wave equations.     

Adsorption and inhibition effect of curcumin on mild steel corrosion in hydrochloric acid

The inhibition effect of curcumin on the corrosion of mild steel in 1.0 M HCl solution was studied by weight loss, potentiodynamic polarization curves and electrochemical impedance spectroscopy (EIS) methods. The experimental results suggest that this compound is an efficient corrosion inhibitor and the inhibition efficiency increases with the increase in inhibitor concentration. Adsorption of this compound on mild steel surface obeys Langmuir isotherm. Also the objective of this work is to attempt to find relationships between electronic structure and inhibition efficiency. The structural parameters, such as the frontier molecular orbital energies (E _HOMO and E _LUMO), gap of energy ΔE, from the molecule to iron as well as electronic parameters such as Mulliken atomic populations were calculated and discussed using the Density Functional Theory method (DFT).     

Scattering matrix for Feshbach-Villars equation for spin 0 and 1/2: Woods-Saxon potential

The Feshbach-Villars equation for spin 0 and 1/2 in the presence of Woods-Saxon potential is solved using an unified approach. The good boundary conditions for jumping potential are found and Klein tunneling and Klein paradox are discussed. The scattering matrix is constructed and the phase shifts, the transmission and reflection coefficients are deduced.     

On the Linear Forms of the Schrödinger Equation

Generalising the linearisation procedure used by Dirac and later by Lévy-Leblond, we derive the first-order non-relativistic wave equations for particles of spin 1 and spin 3/2 starting from the Schrödinger equation. By the introduction in the momentum of a correction linear in coordinates, we establish the wave equation of the radial harmonic oscillator with spin-orbit coupling.     

Path integral for a neutral spinning particle in interaction with a rotating magnetic field and a scalar potential

In this paper we consider a neutral spinning particle in interaction with a linear increasing rotating magnetic field and a scalar harmonic potential using the path integral formalism. The Pauli matrices which describe the spin dynamics are replaced by two fermionic oscillators via the Schwinger’s model. The calculations are carried out explicitly using fermionic exterior current sources. The problem is then reduced to that of a spinning forced harmonic particle whose spin is coupled to exterior derivative current sources. The result of the propagator is given as a series which is exactly summed up by means of the Laplace transformation and the use of some recurrence formula of the oscillator wave functions. The energy spectrum and the corresponding wave functions are also deduced.     

The one-dimensional spinless Salpeter Coulomb problem with minimal length

We present an exact analytical treatment of the semi-relativistic spinless Salpeter equation with a one-dimensional Coulomb interaction in the context of quantum mechanics with modified Heisenberg algebra implying the existence of a minimal length. The problem is tackled in the momentum space representation. The bound-state energy equation and the corresponding wave functions are exactly obtained.     

Path integral for a Dirac particle in a quantized plane wave field

The problem of a relativistic spinning particle interacting with a quantized electromagnetic plane wave is treated by employing path integral methods and introducing the notion of a coherent state action. The dynamics of the particle spin is described using the supersymmetric action proposed recently by Alexandrou et al. in the so-called global representation. It is shown that to obtain the relative causal Green function, two fermionic identities, related directly to the classical equations of motion, have to be incorporated. The Green function, as constructed, allows us to extract in a natural way the expressions of the corresponding energy spectrum and wave functions. Received: 26 July 2002 / Revised version: 11 September 2002 / Published online: 25 October 2002     

Path integral for spinning particle in the plane wave field: Global and local projections

The Green function related to the problem of a Dirac particle interacting with a plane wave is calculated via the path integral formalism proposed recently by Alexandrou et al. according to the two so-called global and local projections. With the help of the incorporation of two simple identities, it is shown that the contribution to the calculation of the integrals comes essentially from classical solutions projected along the direction of wave propagation.