Non-commutative solitons and strong-weak duality

Some properties of the non-commutative versions of the sine-Gordon model (NCSG) and the corresponding massive Thirring theories (NCMT) are studied. Our method relies on the NC extension of integrable models and the master Lagrangian approach to deal with dual theories. The master Lagrangians turn out to be the NC versions of the so-called affine Toda model coupled to matter fields (NCATM) associated to the group GL(2), in which the Toda field belongs to certain representations of either $U(1){x} U(1)$ or $U(1)_{C}$ corresponding to the Lechtenfeld et al. (NCSG$_{1}$) or Grisaru-Penati (NCSG$_{2}$) proposals for the NC versions of the sine-Gordon model, respectively. Besides, the relevant NCMT$_{1, 2}$ models are written for two (four) types of Dirac fields corresponding to the Moyal product extension of one (two) copy(ies) of the ordinary massive Thirring model. The NCATM$_{1,2}$ models share the same one-soliton (real Toda field sector of model 2) exact solutions, which are found without expansion in the NC parameter $\theta$ for the corresponding Toda and matter fields describing the strong-weak phases, respectively. The correspondence NCSG$_{1}$ $\leftrightarrow$ NCMT$_{1}$ is promising since it is expected to hold on the quantum level.Comment: 24 pages, 1 fig., LaTex. Typos in star products of eqs. (3.11)-(3.13) and footnote 1 were corrected. Version to appear in JHE

Computational studies on the behaviour of anionic and nonionic surfactants at the SiO2_{2} (silicon dioxide)/water interface

Molecular dynamics simulations to study the behaviour of anionic (Sodium Dodecylsulfate, SDS) and nonionic (Monooleate of Sorbitan, SPAN80) surfactants close to a SiO$_{2}$ (silicon dioxide) surface were carried out. Simulations showed that a water layer was first adsorbed on the surface and then the surfactants were attached on that layer. Moreover, it was observed that water behaviour close to the surface influenced the surfactant adsorption since a semi-spherical micelle was formed on the SiO$_{2}$ surface with SDS molecules whereas a cylindrical micelle was formed with SPAN80 molecules. Adsorption of the micelles was conducted in terms of structural properties (density profiles and angular distributions) and dynamical behaviour (diffusion coefficients) of the systems. Finally, it was also shown that some water molecules moved inside the solid surface and located at specific sites of the solid surface.Comment: 8 pages, 6 fiigure