Interactions of large amplitude solitary waves in viscous fluid conduits

The free interface separating an exterior, viscous fluid from an intrusive conduit of buoyant, less viscous fluid is known to support strongly nonlinear solitary waves due to a balance between viscosity-induced dispersion and buoyancy-induced nonlinearity. The overtaking, pairwise interaction of weakly nonlinear solitary waves has been classified theoretically for the Korteweg-de Vries equation and experimentally in the context of shallow water waves, but a theoretical and experimental classification of strongly nonlinear solitary wave interactions is lacking. The interactions of large amplitude solitary waves in viscous fluid conduits, a model physical system for the study of one-dimensional, truly dissipationless, dispersive nonlinear waves, are classified. Using a combined numerical and experimental approach, three classes of nonlinear interaction behavior are identified: purely bimodal, purely unimodal, and a mixed type. The magnitude of the dispersive radiation due to solitary wave interactions is quantified numerically and observed to be beyond the sensitivity of our experiments, suggesting that conduit solitary waves behave as "physical solitons." Experimental data are shown to be in excellent agreement with numerical simulations of the reduced model. Experimental movies are available with the online version of the paper.Comment: 13 pages, 4 figure

Generation of Hyperentangled Photons Pairs

We experimentally demonstrate the first quantum system entangled in every degree of freedom (hyperentangled). Using pairs of photons produced in spontaneous parametric downconversion, we verify entanglement by observing a Bell-type inequality violation in each degree of freedom: polarization, spatial mode and time-energy. We also produce and characterize maximally hyperentangled states and novel states simultaneously exhibiting both quantum and classical correlations. Finally, we report the tomography of a 2x2x3x3 system (36-dimensional Hilbert space), which we believe is the first reported photonic entangled system of this size to be so characterized.Comment: 5 pages, 3 figures, 1 table, published versio

A six-coordinate aryl-germanium complex formed by the Kläui ligand

PhGeCl₃ reacts with Na{[OP(OEt)₂]₃CoCp} to give the six-coordinate complex PhCl₂Ge{[OP(OEt)₂]₃CoCp}, characterised spectroscopically and by an X-ray crystal structure determination which showed a firmly-attached tridentate ligand [Ge–O 1.973(2) Å]

Novel six-coordinate Aryl- and Alkyltin complexes

Organo-tin compounds have wide applications as pesticides and as intermediates for organic synthesis.¹ They are invariably Sn(IV) derivatives and are generally four-coordinate.² The mixed organo/chioro compounds of the type RnSnCI4-n do however have the ability to expand their coordination numbers to five or six. This depends critically on the substituents - with four organic groups, R₄Sn, there is no tendency at all to coordinate extra ligands, while at the other extreme SnCl₄ readily forms six-coordinate [SnC1₄L₂] complexes since the electronegative halo groups increase the Lewis acidity of the tin centre