Homoclinic bifurcations in low-Prandtl-number Rayleigh-B\'{e}nard convection with uniform rotation

We present results of direct numerical simulations on homoclinic gluing and ungluing bifurcations in low-Prandtl-number ($0 \leq Pr \leq 0.025$) Rayleigh-B\'{e}nard system rotating slowly and uniformly about a vertical axis. We have performed simulations with \textit{stress-free} top and bottom boundaries for several values of Taylor number ($5 \leq Ta \leq 50$) near the instability onset. We observe a single homoclinic ungluing bifurcation, marked by the spontaneous breaking of a larger limit cycle into two limit cycles with the variation of the reduced Rayleigh number $r$ for smaller values of $Ta (< 25)$. A pair of homoclinic bifurcations, instead of one bifurcation, is observed with variation of $r$ for slightly higher values of $Ta$ ($25 \leq Ta \leq 50$) in the same fluid dynamical system. The variation of the bifurcation threshold with $Ta$ is also investigated. We have also constructed a low-dimensional model which qualitatively captures the dynamics of the system near the homoclinic bifurcations for low rotation rates. The model is used to study the unfolding of bifurcations and the variation of the homoclinic bifurcation threshold with $Pr$.Comment: 6 pages, 7 figures, 1 tabl

Effect of a weak longitudinal modulation in refractive index on transverse localization of light in 1D disordered waveguide lattices

We report the enhancement of the effect of transverse localization of light (TL) in presence of a weak longitudinal modulation of refractive index in disordered waveguide lattices. In our chosen lattices, tunneling inhibition along length favors to achieve the diffraction-free propagation along with the simultaneous presence of transverse disorder. Results will be useful to tune the threshold value of disorder to achieve localized light.Comment: 4 pages. arXiv admin note: text overlap with arXiv:1204.614