Decay of confined,two-dimensional,spatially periodic arrays of vortices: A numerical investigation

The disarrangement of a perturbed lattice of vortices was studied numerically. The basic state is an exponentially decaying, exact solution of the Navier-Stokes equations. Square arrays of vortices with even numbers of vortex cells along each side were perturbed and their evolution was investigated. Whether the energy in the perturbation grows somewhat before it decays or decays monotonically depends on the initial strength of the vortices of the basic state, the extent of lateral confinement and the structure of the perturbation. The critical condition for temporally local instability, i.e. the critical amplitude of the basic state that must be exceeded to allow energy transfer from the basic state to the perturbation, is discussed. In the strongly confined case of a square lattice of four vortices the appearance of enchancement of global rotation is the result of energy transfer from the basic state to a temporally local unstable mode. Energy is transferred from the basic state to larger-scaled structures (inverse cascade) only if the scales of the larger structures are inherently contained in the initial structure of the perturbation. The initial structure of the double array of vortices is not maintained except for a very special form of perturbation. The facts that large scales decay more slowly than small scales and that, when non-linearities are sufficiently strong, energy is transferred from one scale to another explain the differences in the disarrangement process for different initial strengths of the vortices of the basic state. The stronger vortices, i.e. the vortices perturbed in a manner that increases their strength, tend to dominate the weaker vortices. The pairing and subsequent merging (or capture) of vortices of like sense into larger-scale vortices are described in terms of peaks in the evolution of the square root of the palinstrophy divided by the enstrophy.     

Cosmological models in the scalar-tetradic theory B

We present two methods for solving the cosmological equations of the scalar-tetradic theory B [19] when a Friedmann-Robertson-Walker (FRW) geometry is assumed. Among the many solutions found there are several physically meaningful ones including inflationary universe solutions.     

Single electron tunneling rates in multijunction circuits

The rate of electron tunneling through normal metal tunnel junctions is calculated for the case of ultrasmall junction capacitances. The so-called Coulomb blockade of electron tunneling at low temperatures is shown to be strongly affected by the external electrical circuit. Under the common experimental condition of a low impedance environment the Coulomb blockade is suppressed for single tunnel junctions. However, a Coulomb gap structure emerges for junctions embedded in a high impedance environment. For a double junction setup a Coulomb blockade of tunneling arises even for low impedance environments due to the charge quantization on the metallic island between the junctions. An approach using circuit analysis is presented which allows to reduce the calculation of tunneling rates in multijunction circuits to those of a single junction in series with an effective capacitance. The range of validity of the socalled local rule and global rule rates is clarified. It is found that the tunneling rate tends towards the global rule rate as the number of junctions is increased. Some specific results are given for a one-dimensional array of tunnel junctions.     

The behavior of cracked cross-ply composite laminates under shear loading

An interlaminar-shear-stress analysis developed earlier by Tsai et al. (1990, Micro-cracking-Induced Damage in Composites) for a [φ_m/θ_n], bi-directional composite laminate is used to solve the case of a cross-ply [0_m/90_n]_x laminate with the 90° layer only or both layers cracked under pure shear loading. Strains, forces and laminate shear modulus reduction due to matrix cracking were obtained. Experimental results for shear modulus as a function of crack densities were obtained by a simple shear test and they agree very well with the theoretical prediction.     

Modélisation du champ des vitesses de l'urine dans un bolus urétéralModelling of urine flow in an ureteral bolus

Urine transport is made from the kidney to the bladder through the ureter by isolated pockets called bolus. To determine the urine flow in a bolus, we use an adherence condition on the interface urine/wall. It gives us an infinite linear system verified by a set of parameters. An iterative and convergent algorithm allows us to solve this system and to determine analytically the components of the velocity vector in the bolus. To cite this article: A. Vogel et al., C. R. Mecanique 332 (2004).     

Boundaries for algebras of holomorphic functions

Let A_u(B_G) be the Banach algebra of all complex valued functions defined on the closed unit ball B_G of a complex Banach space G which are uniformly continuous on B_G and holomorphic in the interior of B_G, endowed with the sup norm. A characterization of the boundaries for A_u(B_G) is given in case G belongs to a class of Banach spaces that includes the pre-dual of a Lorentz sequence space studied by Gowers in Israel J. Math. 69 (1990) 129-151. The non-existence of the Shilov boundary for A_u(B_G) is also proved.     

An analytical proof of Hardy-like inequalities related to the Dirac operator

We prove some sharp Hardy-type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.     

C D : a computer program to generate 1D, 2D and 3D grids of functions dependent on the molecular ab initio electron density

A program to compute many functions dependent on the electron density ρ(r) from the results of ab initio molecular calculations is presented. The program allows the generation of different one-, two-, and three-dimensional grids for further graphical representation or numerical analysis. Other options like extracting separate atom contributions to the function computed or locating maximum and minimum values are also implemented. A number of illustrative applications regarding different ρ(r)-dependent functions are presented and the performance and portability of the program is discussed.