Surfactant driven flows overlying a hydrophobic epithelium: film rupture in the presence of slip

Both for tear films and along the airways within the lung, one has an extremely thin fluid layer overlying a biological substrate; in both cases surfactants either of natural origin, or artificially introduced, are important in driving fluid flows. There is evidence that slip can occur when hydrophilic liquids, similar to mucus or aqueous tear films, overlie hydrophobic epithelium. Utilizing results from recent experimental findings we examine the possible influence of slip upon tear film rupture, important in so-called dry eye, and upon surfactant-induced flows within the lung, used in surfactant replacement therapy.     

Interchange of infimum and integral

We prove a new interchange theorem of infimum and integral. Its distinguishing feature is, on the one hand, to establish a general framework to deal with interchange problems for nonconvex integrands and nondecomposable sets, and, on the other hand, to link the theorems of Rockafellar and Hiai-Umegaki with the one of Bouchitté-Valadier. We give an application to relaxation of nonconvex geometric integrals of Calculus of Variations.Received: 20 March 2002, Accepted: 12 March 2003, Published online: 16 May 2003     

Energy Levels of Neutral Atoms Via a New Perturbation Method

The energy levels of neutral atoms supported by potential V (r) = -Zexp(-ar)/r (Yukawa potential) are studied, using both dimensional and dimensionless quantities, via a new analytical methodical proposal (devised to solve for nonexactly solvable Schrödinger equation). Using dimensionless quantities, by scaling the radial Hamiltonian through y = Zr and = /Z, we report that the scaled screening parameter is restricted to have values ranging from zero to less than 0.4. On the other hand, working with the scaled Hamiltonian enhances the accuracy and extremely speeds up the convergence of the energy eigenvalues. The energy levels of several new eligible scaled screening parameter values are also reported.     

Low-energy effects in brane worlds: Liennard–Wiechert potentials and Hydrogen Lamb shift

Testing extra dimensions at low-energies may lead to interesting effects. In this work a test point charge is taken to move uniformly in the 3D subspace of a (3 + n)-brane embedded in a (3 + n + 1)-space with n compact and one warped infinite spatial extra dimensions. We found that the electromagnetic potentials of the point charge match standard Liennard–Wiechert’s at large distances but differ from them close to it. These are finite at the position of the charge and produce finite self-energies. We also studied a localized Hydrogen atom and take the deviation from the standard Coulomb potential as a perturbation. This produces a Lamb shift that is compared with known experimental data to set bounds for the parameter of the model. This work provides details and extends results reported in a previous Letter. We are pleased to dedicate this work to Professor Octavio Obregón on occasion of his 60th birthday. H. A. Morales-Técotl is an associate member of the Abdus Salam ICTP, Trieste Italy.     

Unconditionally Stable Complex Envelope Wave Equation PML Algorithm for Band Limited FDTD Simulations

Unconditionally stable complex envelope (CE) perfectly matched layer (PML) absorbing boundary conditions (ABCs) are presented for truncating the scalar wave-equation finite difference time domain (WE-FDTD) grids. The formulations are based on incorporating the alternating direction implicit (ADI) scheme into the CE FDTD implementations of the scalar wave-equation derived in the PML region at the domain boundaries. Numerical example carried out in two dimensional domain shows that the proposed formulations are more accurate than the classical ADI scalar wave equation PML formulations when it is used for modelling band limited electromagnetic applications.     

Pretreatment effects on the electrochemical responses for aluminium–magnesium alloy AA5083 corrosion behaviour

Electrochemical investigations on aluminium alloy corrosion in a sodium chloride solution have been performed by potentiostatic and potentiodynamic (electrochemical impedance spectroscopy) methods. Measurements have been obtained after mechanical polishing or electrochemical stripping in deaerated or not solution. All the results are strongly depending on the pretreatments that are undergone in the laboratory before the experimental measurements. Mechanical polishing induces huge effects on the surface of the analysed samples and a long time is necessary to avoid the effects of this treatment; instead, an electrochemical cleaning does not modify the surface and results can be regarded more rapidly as significant of the surface with higher reproducibility.     

Unconditionally Stable Z-Transform ADI-PML Algorithm for Lorentzian Double Negative Meta-Materials

Unconditionally stable formulations of the anisotropic perfectly matched layer (APML) are presented for truncating double negative (DNG) meta-material finite difference time domain (FDTD) grids. In the proposed formulations, the Z-transform theory is employed in the alternating direction implicit FDTD (ADI-FDTD) scheme to obtain update equations for the field components in the DNG meta-material domains. Numerical examples carried out in one dimensional Lorentzian type DNG meta-material domains are included to show the validity of the proposed formulations.     

Selecting an Effective Entropy Estimator for Short Sequences of Bits and Bytes with Maximum Entropy

Entropy makes it possible to measure the uncertainty about an information source from the distribution of its output symbols. It is known that the maximum Shannon’s entropy of a discrete source of information is reached when its symbols follow a Uniform distribution. In cryptography, these sources have great applications since they allow for the highest security standards to be reached. In this work, the most effective estimator is selected to estimate entropy in short samples of bytes and bits with maximum entropy. For this, 18 estimators were compared. Results concerning the comparisons published in the literature between these estimators are discussed. The most suitable estimator is determined experimentally, based on its bias, the mean square error short samples of bytes and bits.     

New complexes of Zn(II) with the anti-inflammatory non-steroidal drug,ibuprofen and nitrogen donor ligands. Synthesis,characterization and biological activity

Complexes of [Zn(ibup)₂(4,4′-bipy)]_n 1, [Zn(ibup)₂(phen)] 2, [Zn(ibup)₂(2,9-dmphen)] 3, [Zn(ibup)₂(1,2-dmimidazole)₂] 4, and [Zn(ibup)₂(2-am-6-picoline)₂] 5 (ibu = ibuprofen, 4,4′-bipy = 4,4′-bipypyridine, phen = 1,10-phenanthroline, 2,9-dmephen = 2,9-dimethyl-1,10-phenanthroline, 1,2-dmimidazole = 1,2-dimethylimidazole, and 2-am-6-picoline = 2-amino-6-picoline) were prepared and characterized. The crystal structure of 1 was determined by single-crystal X-ray diffraction. The in vitro anti-bacterial activities for the complexes against Gram-positive (Micrococcus luteus, Staphylococcus aureus and Bacillus subtilis) and Gram-negative (Escherichia coli, Klebsiella pneumonia and Proteus mirabilis) bacteria were done using the agar well-diffusion method. Complexes 1–3 showed anti-bacterial activity against Gram-positive bacteria, while 4 and 5 did not exhibit anti-bacterial activity. Complexes 2 and 3 were selected for further studies. Complexation of zinc-ibuprofen with phen as in 2 decreased the anti-bacterial activity against most of the bacteria used. The complexation in 3 decreased the anti-bacterial activity in Gram-positive bacteria but for Gram-negative bacteria, the overall anti-bacterial activity of uncoordinated 2,9-dmphen was enhanced upon coordination with zinc ibuprofen.