Coupled frequencies of a rectangular hydroelastic system with two fluids

This paper deals with the study of behaviour of an idealized 2D hydroelastic system involving two inviscid liquids with an elastic rectangular container. The main objective is to investigate the influence of the physical parameters on eigenfrequencies and eigenmodes of the system. The study extends the previous results obtained for hydroelastic systems with one fluid. The governing equations describing the behaviour of the system are analyzed by using the concept of normal modes and their solutions presented in the form of infinite series. The expansion coefficients for the velocity potentials are calculated by employing a new inner product that allows the orthogonalisation of the normal modes. An eigenfrequency equation is then derived from the existence condition of a nontrivial solution. The numerical calculations are performed by varying only some relevant parameters.     

A new method for the calculation of steady periodic capillary-gravity waves on water of arbitrary uniform depth

This paper presents a method for the calculation of steady periodic capillary-gravity waves on water of arbitrary uniform depth. The method developed by Debiane and Kharif in 1997 for infinite depth is extended to finite depth. The water-wave problem is reduced to a system of nonlinear algebraic equations which is solved using Newton's method. For the resonant configurations, the method does not suffer from the Wilton's failures and is valid for all depths. In addition, it is shown that the method allows the computation of solitary waves and generalized solitary waves.     

Intramolecular hydrogen bonding in structural conformers of 2‐amino methylene malonaldehyde: AIM and NBO studies

The molecular structure and intramolecular hydrogen bond energies of 44 conformers of 2‐Amino methylene malonaldehyde were investigated at MP2 and B3LYP levels of theory using the standard 6‐311++G** basis set and AIM and NBO analysis. The calculated geometrical parameters and conformational analysis in gas phase show that the closed ring via intramolecular hydrogen bonded conformers of this compound are more stable than the other ones. Hydrogen bond energies for H‐bonded conformers were obtained from the related rotamers method (RRM) and Schuster method, and also the nature of H‐bonding of them has been investigated by means of the Bader theory of atoms in molecules, which is based on topological properties of the electron density. Delocalization effects can be identified from the presence of off diagonal elements of the Fock matrix in the NBO basis. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Solvent-free microwave extraction and hydrodistillation of essential oils from endemic Origanum husnucanbaseri H. Duman, Aytac & A. Duran: comparison of antibacterial activity and contents

The essential oils (EOs) obtained by solvent-free microwave extraction (SFME) and hydrodistillation (HD) from endemic Origanum husnucanbaseri H. Duman, Aytac & A. Duran were investigated using the gas chromatography-mass spectrometry system. The main constituents of both oils obtained from SFME and HD from O. husnucanbaseri are borneol (15.2-12.8%), α-terpineol (12.3-10.8%) and trans-sabinene hydrate (11.8-9.92%). The EO obtained from SFME contained substantially higher amounts of oxygenated compounds and lower amounts of monoterpenes than that from HD. The antibacterial activities of the EOs from SFME and HD were evaluated by the disc diffusion method against six bacterial strains. The EO extracted by SFME was more effective than the EO extracted by HD against the tested bacteria, except for Klebsiella pneumoniae American type culture collection (ATCC) 13883. Streptococcus pyogenes ATCC 19615 and Staphylococcus aureus ATCC 25923 in particular were more sensitive against the EO extracted by SFME.     

On the finite generation of the effective monoid of rational surfaces

We give a numerical criterion for ensuring the finite generation of the effective monoid of the surfaces obtained by a blowing-up of the projective plane at the supports of zero dimensional subschemes assuming that these are contained in a degenerate cubic. Furthermore, this criterion also ensures the regularity of any numerically effective divisor on these surfaces. Thus the dimension of any complete linear system is computed. On the other hand, in particular and among these surfaces, we obtain ringed rational surfaces with very large Picard numbers and with only finitely many integral curves of strictly negative self-intersection. These negative integral curves except two (−1)-curves are all contained in the support of an anticanonical divisor. Thus almost all the geometry of such surfaces is concentrated in the anticanonical class.     

Homogenization of an incompressible viscous flow in a porous medium with double porosity

We study the homogenization of an incompressible viscous flow in a porous medium with double porosity. We derive a macroscopic model with local Navier–Stokes system in the large cavities, Darcy law in the thinner porous rock, and a contact law between the two. We use Γ-convergence methods associated with multi-scale convergence notions in order to get this limit law. We exhibit a critical ratio between the two scales of the pores.