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     

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.     

Viscosity Results for a Class of Evolution Inclusions with Maximal Monotone Operators

In the finite dimensional setting, we investigate the existence of viscosity subsolutions of Hamilton–Jacobi–Bellman equations related to control problems subject to evolution inclusions governed by time-dependent maximal monotone operators with Young measures.     

Fine Spectral Analysis of Isotropic Partly Elastic Neutron Transport Operators

This paper deals with spectral theory of a new class of neutron transport operators involving collision operators of the form \(K=K_{i}+K_{e}\) where \(K_{i}\) (resp. \(K_{e}\)) describes the inelastic (resp. elastic) collisions of neutrons with the host material. We give a fine analysis of their asymptotic point spectra for isotropic space homogeneous cross sections in bounded geometries. We provide a new formalism relying on spectral analysis of some non compact symmetrizable operators arising in transport theory. Additional results on essential spectra are also given.     

Glass transition (Tg) and dielectric loss in Na3PO4–Pb3(PO4)2–BiPO4 phosphate glasses

Thermal and dielectric loss properties of Na₃PO₄-Pb₃(PO₄BiPO₄ (Na₂O-PbO-Bi₂O₃-P₂O₅) phosphate glasses, have been studied by the differential scanning calorimetry (DSC) and electrical factor loss (tgδ) measurements. Experiments have been carried out from ambient temperature to 500°C and show a strong influence of sodium ions on T_g and tgδ.